A.T. Robertson Commentary Matthew 27:32

"And as they came out, they found a man of Cyrene, Simon by name: him they compelled to go [with them], that he might bear his cross." — Matthew 27:32 (ASV)

Compelled (ηγγαρευσαν). This word of Persian origin was used in Mt 5:41, which see. There are numerous papyri examples of Ptolemaic date and it survives in modern Greek vernacular. So the soldiers treat Simon of Cyrene (a town of Libya) as a Persian courier (αγγαρος) and impress him into service, probably because Jesus was showing signs of physical weakness in bearing his own Cross as the victims had to do, and not as a mere jest on Simon. "Gethsemane, betrayal, the ordeal of the past sleepless night, scourging, have made the flesh weak" (Bruce). Yes, and the burden of sin of the world that was breaking his heart.

His cross (τον σταυρον αυτου). Jesus had used the term cross about himself (16:24). It was a familiar enough picture under Roman rule. Jesus had long foreseen and foretold this horrible form of death for himself (Matthew 20:19; Matthew 23:24; Matthew 26:2). He had heard the cry of the mob to Pilate that he be crucified (27:22) and Pilate's surrender (27:26) and he was on the way to the Cross (27:31). There were various kinds of crosses and we do not know precisely the shape of the Cross on which Jesus was crucified, though probably the one usually presented is correct. Usually the victim was nailed (hands and feet) to the cross before it was raised and it was not very high. The crucifixion was done by the soldiers (27:35) in charge and two robbers were crucified on each side of Jesus, three crosses standing in a row (27:38).