Is. 40:28 Hast thou not known? hast thou not heard, that the everlasting God, the LORD, the Creator of the ends of the earth, fainteth not, neither is weary?
Pretty clear, but the Skeptics have a few in reply. Let's first note the words: "fainteth" is ya'aph, while "weary" is yaga. Now then:
Exodus 31:17 It is a sign between me and the children of Israel for ever: for in six days the LORD made heaven and earth, and on the seventh day he rested, and was refreshed.
A need for rest? No -- "rested" simply means "desisted from exertion", i.e., stopped what one was doing. The Hebrew word for "rest" (shabath) is used in the context of something ceasing or lacking, or in the sense of celebration (see Lev. 2:13; 23:32; the Greek in Heb. 4:4 has similar meaning.)
"Refreshed" literally means "breathed" -- this word is used only 3 times in the OT, once in reference to people on the Sabbath (Ex. 23:12) and once at 2 Sam. 16:14, "And the king, and all the people that were with him, came weary, and refreshed themselves there."
Does it mean one needs a nap? Only if the context demands it, as in the latter case. The word actually suggests more of a sense of satisfaction as derived from a cooling air, as is appropos for the seventh day (Gen. 1:31, And God saw every thing that he had made, and, behold, it was very good. -- an evaluation of what was before it.) If tiredness was what was at issue, a better word would have been ravach, or "breathe freely."
Is. 1:14 Your new moons and your appointed feasts my soul hateth: they are a trouble unto me; I am weary to bear them.
Even by itself, it's hard to see how this would give any idea that God was physically tired, and the word bears it out: it is la'ah, meaning disgusted. (This word is also used in Jer. 15:6.)
Harder is this one:
Is. 43:24 Thou hast bought me no sweet cane with money, neither hast thou filled me with the fat of thy sacrifices: but thou hast made me to serve with thy sins, thou hast wearied me with thine iniquities.
This time it is yaga, but there's a poetic point to make, though not what Skeptics might expect.
This is made in counter-point to Is. 43:23, "Thou hast not brought me the small cattle of thy burnt offerings; neither hast thou honoured me with thy sacrifices. I have not caused thee to serve with an offering, nor wearied thee with incense." 43:24 is a rhetorical hyperbole, making the point that none of God's demands upon the people were the sort to wear them out, and God counterpointing -- with heavy sarcasm -- "No, you have worn me out with your sins."
This is a powerful indictment in light of that God said in 40:28 that he does not get weary.