An affirmative answer to this question underpins Christopher and Richard Hays’ book The Widening of God’s Mercy:

‘Contrary to the common idea that God’s decisions are eternal and immutable, there are numerous stories of God changing God’s mind in the Bible, and others in which God declares that past judgments were too extreme.’

On the basis of this, the authors develop a ‘trajectory’ argument, according to which sexual behaviours once rejected by God in Scripture have now become acceptable.

Of course, these supposed ‘changes of mind’ are not thought to be arbitrary.  Rather,

‘God repeatedly changes his mind in ways that expand the sphere of his love, preserve his relationship with humankind, and protect and show mercy toward them.’

But what are we to make of the fundamental assertion: ‘Scripture teaches that God is capable of changing his mind’?

First, we must reckon with those repeated statements in Scripture that God does not change his mind:

Num 23:19 God is not a man, that he should lie,
nor a human being, that he should change his mind.
Has he said, and will he not do it?
Or has he spoken, and will he not make it happen?

1 Sam 15:29 “The Preeminent One of Israel does not go back on his word or change his mind, for he is not a human being who changes his mind.”

Eze 24:14 “ ‘I the LORD have spoken; judgment is coming and I will act! I will not relent, or show pity, or be sorry!”

Mal 3:6 “Since, I, the LORD, do not go back on my promises, you, sons of Jacob, have not perished.”

Heb 7:20 ‘The others have become priests without a sworn affirmation, 7:21 but Jesus did so with a sworn affirmation by the one who said to him, “The Lord has sworn and will not change his mind, ‘You are a priest forever’ ”—7:22 accordingly Jesus has become the guarantee of a better covenant.’ (Quoting Psa 110:4)

James 1:17 ‘All generous giving and every perfect gift is from above, coming down from the Father of lights, with whom there is no variation or the slightest hint of change. 1:18 By his sovereign plan he gave us birth through the message of truth, that we would be a kind of firstfruits of all he created.’

Second, for God to change his mind would be for him to act contrary to his very nature.  According to Stephen Charnock, human beings change their minds either because of a lack of foresight or because of unreasonableness or instability on their part.  But neither of these can be attributed to God.

Third, if God were to change his mind then disastrous consequences would follow.  He would not be a God who could be relied upon.  We couldnever be sure that we were living in accordance with his will.

What, then, should we make of those scriptural texts which seem to suggest that God does, in fact, change his mind?

Gen 6:6 ‘The LORD regretted that he had made humankind on the earth, and he was highly offended. 6:7 So the LORD said, “I will wipe humankind, whom I have created, from the face of the earth—everything from humankind to animals, including creatures that move on the ground and birds of the air, for I regret that I have made them.”’

1 Sam 15:11 “I regret that I have made Saul king, for he has turned away from me and has not done what I told him to do.”

Jon 3:10 ‘When God saw their actions—they turned from their evil way of living!—God relented concerning the judgment he had threatened them with and he did not destroy them.  4:1 This displeased Jonah terribly and he became very angry. 4:2 He prayed to the LORD and said, “Oh, LORD, this is just what I thought would happen when I was in my own country. This is what I tried to prevent by attempting to escape to Tarshish!—because I knew that you are gracious and compassionate, slow to anger and abounding in mercy, and one who relents concerning threatened judgment.’

See also Ex 32:10-14, Isa 38:1-6 and Amos 7:1-3.

By way of response, we need to say, with Aquinas, that all language about God is analogical.  So repentance, for example, does not mean the same when applied to God as it does when applied to us.  God’s mind and will are unchangeable, but they have different results, depending on human behaviour.

[The above is based on this, by Martin Davie]

Geisler and Howe (When Critics Ask): Any change must be either for the better or for the worse.  Since God is perfect, he cannot change for the better, and if he were to change for the worse he would not be God.  They further argue that any change of mind would be in the light of new information or insights, but in God’s case to do so would impeach his omniscience.  Therefore, any alteration in God’s attitude or actions must be due, not to a change within himself, but to the reaction of his perfect and unchanging nature to changed circumstances.  It is the circumstances that have change, not God.

Reymond (A New Systematic Theology of the Christian Faith): It is mistaken to think of God as immobile or adopting an ‘eternally frozen pose’ (Packer).  His immutability is not static, but dynamic.  The God of the Bible is forever acting and reacting.

Berkhof (Systematic Theology): Divine immutability does not imply immobility.  God enters into manifold relations with humankind.  They change, but he changes not.  There is change in his relations with us, but no change in his being, attributes, purpose, motives, or promises.

Packer (Knowing God): Those texts which speak of God ‘repenting’ refer to a change in his previous treatment of specific people, as a result of their reaction to that treatment.  There is no indication that this reaction took God by surprise, or implied any change in his eternal purpose.

A.W. Pink (cited by Packer, Knowing God): We change our minds and reverse our plans either because of lack of foresight or lack of ability.  Since God is both omniscient and omnipotent, he never needs to change his mind.

Kaiser (Hard Sayings of the Bible): God is unchanging in his essence and character.  But many of his promises and warnings are conditional.  The classic example is Jer 18:7-10 –

18:7 ‘There are times, Jeremiah,14 when I threaten to uproot, tear down, and destroy a nation or kingdom.15 18:8 But if that nation I threatened stops doing wrong,16 I will cancel the destruction17 I intended to do to it. 18:9 And there are times when I promise to build up and establish18 a nation or kingdom. 18:10 But if that nation does what displeases me and does not obey me, then I will cancel the good I promised to do to it.’

God’s response to us changes as we ourselves change either in the direction of sin or of holiness.  God’s unchangeableness does not imply transcendent detachment from people and events; he is capable of experiencing regret and grief.  However, his changing responses to us do not reflect on his essential happiness and blessedness:

‘The point is that unchangeableness must not be thought of as if it were some type of frozen immobility. God is not some impervious being who cannot respond when circumstances or individuals change. Rather, he is a living person, and as such he can and does change when the occasion demands it. He does not change in his character, person or plan. But he can and does respond to our changes.’

Preston Sprinkle: Hays and Hays claim that in Jer 18:7-10 ‘the prophet may announce judgment only to have God change his mind about it.’  But this misrepresents the text: ‘There’s a big difference between God not judging people who repent and God changing his mind about whether a sin deserves judgment.’

R.A. Torrey (Difficulties in the Bible): Illustrates: a railway station, though stationary, changes its position relative to a train that is passing through.