This is a rather common question asked by pseudo-intellectuals who think they have stumbled across a great chink in the Christian’s belief about the omnipotence of God. The answer to the question is quite simply, “No, there are many things God cannot do.”
For one thing, he cannot do something that is logically impossible such as make a rock so big He cannot lift it. Neither can he draw a square circle. For that matter, He can not do something that is impossible. Because the moment he accomplished the feat, it would no longer be impossible since He proved it was possible for Him.
But we don’t have to stoop to such nonsense to find things God cannot do. The Bible clearly says it is “impossible for God to lie” (Hebrews 6:18) and that “He cannot deny himself” (2 Timothy 2:13), meaning violate His own nature or integrity. He can not stop being God. He can not stop being good. He cannot cease to exist – since existence is a component of goodness. I could go on and on listing things God can not do but I think you grasp the concept.
When Christians speak of God’s omnipotence or when Jesus assures us that “with God all things are possible” (Matthew 19:26) we are not referring to either ludicrous scenarios that parade as profound discoveries of truth nor to things that would violate God’s very nature and character. Omnipotent is understood to be “possessing all power”. Simply put, that means God can do anything that can be done. He has the ability to perform any feat consistent with His character and nature.
This is one reason it is so vital that believers study the Word to know what God says about Himself and the world around us. As believers, we appear foolish when we try to defend God and ascribe to Him attributes that He does not even claim for Himself. “Study to show yourself approved unto God, a workman that does not need to be ashamed, rightly dividing the word of truth.” (2 Timothy 2:15)