This question is frequently asked by skeptics of God, the Bible, Christianity, etc. If God can create a rock that He cannot lift, then God is not omnipotent. If God cannot create a rock so heavy that He cannot lift it, then God is not omnipotent. According to this argument, omnipotence is self-contradictory. Therefore, God cannot be omnipotent. So, the question, could God create a rock so heavy He could not lift it? The quick answer is “No.” But the explanation is far more important to understand than the answer...
This question is based on a popular misunderstanding about the definitions of words like “almighty” or “omnipotent.” These terms do not mean that God can do anything. Rather, they describe the amount of God’s power. Power is the ability to effect change - to make something happen. God (being unlimited) has unlimited power, and the Bible affirms this (Job 11:7-11, 37:23; 2 Corinthians 6:18; Revelation 4:8; etc.). Therefore, God can do whatever is possible to be done. God cannot, however, do that which is actually impossible. This is because true impossibility is not based on the amount of power one has, it is based on what is really possible. The truly impossible is not made possible by adding more power. Therefore, unless context indicates otherwise (e.g. Matthew 19:26 where man’s ability is being shown in contrast to God’s), impossibility means the same thing whether or not God is involved.
So, the first part of the question is based on a false idea—that God being almighty means that He can do anything. In fact, the Bible itself lists things God cannot do - like lie or deny Himself (Hebrews 6:18; 2 Timothy 2:13; Titus 1:2). The reason He cannot do these things is because of His nature and the nature of reality itself. God cannot do what is not actually possible to be done, like creating a two-sided triangle, or a married bachelor. Just because words can be strung together this way does not make the impossible possible—these things are contradictions, they are truly impossible in reality. Now, what about this rock? A rock would have to be infinitely large to defeat an infinite amount of lifting power. But an infinite rock is a contradiction since material objects cannot be infinite. Only God is infinite. There cannot be two infinites. So the question is actually asking if God can make a contradiction—which He cannot.