This text clearly occupies substitutionary language. This passage foretold Christ bearing the sins of man upon Himself. He was offered up in the same manner as an unblemished lamb for our sins (1 Peter 1:18-19). His innocent blood was shed for us (1 Peter 3:18). Our sins are forgiven by His wounds (1 Peter 2:24). The Apostle Paul in Philippians 2:7-8 alludes to the humility of the suffering servant (Isaiah 53:7). The idea of vicarious atonement finds its basis in the sacrifices performed under the Mosaic Law:
"When he finishes atoning for the holy place and the tent of meeting and the altar, he shall offer the live goat. Then Aaron shall lay both of his hands on the head of the live goat, and confess over it all the iniquities of the sons of Israel and all their transgressions in regard to all their sins; and he shall lay them on the head of the goat and send it away into the wilderness by the hand of a man who stands in readiness. The goat shall bear on itself all their iniquities to a solitary land; and he shall release the goat in the wilderness." (Leviticus 16:20-22)
Animals paid the price for the sins of people with their own lives. They did nothing to deserve their fate. Thus, animals served as an innocent substitute in the place of men. Though animal sacrifices temporarily held off the judgement of God, the Levitical sacrificial system pointed to the one perfect sacrifice of Jesus Christ (Hebrews 10:1-2). Richard L. Mayhue provides this helpful synopsis of Isaiah 53 emphasizing the substitutionary elements contained therein:
"1. v. 4 - "our griefs He...bore" 2. v. 4 - "our sorrows He carried" 3. v. 5 - "He was pierced... for our transgressions" 4. v. 5 - "He was crushed for our iniquities" 5. v.5 - "by His scourging we are healed" 6. v. 6 - "caused the iniquity of us all to fall on Him" 7. v. 8 - "He was cut off...for the transgression of my people" 8. v. 11 - "He will bear their iniquities" 9. v. 12 - "He Himself bore the sin of many"
The New English Translation has this footnote on Isaiah 53:5:
"tn The preposition מִן (min) has a causal sense (translated “because of”) here and in the following clause. tn Heb “the punishment of our peace [was] on him.” שָׁלוֹם (shalom, “peace”) is here a genitive of result, i.e., “punishment that resulted in our peace.”sn Continuing to utilize the imagery of physical illness, the group acknowledges that the servant’s willingness to carry their illnesses (v. 4) resulted in their being healed. Healing is a metaphor for forgiveness here."
The New English Translation has this footnote on Isaiah 53:6:
"tn Elsewhere the Hiphil of פָגַע (paga’) means “to intercede verbally” (Jer 15:11; 36:25) or “to intervene militarily” (Isa 59:16), but neither nuance fits here. Apparently here the Hiphil is the causative of the normal Qal meaning, “encounter, meet, touch.” The Qal sometimes refers to a hostile encounter or attack; when used in this way the object is normally introduced by the preposition -בְּ (bet, see Josh 2:16; Judg 8:21; 15:12, etc.). Here the causative Hiphil has a double object—the Lord makes “sin” attack “him” (note that the object attacked is introduced by the preposition -בְּ. In their sin the group was like sheep who had wandered from God’s path. They were vulnerable to attack; the guilt of their sin was ready to attack and destroy them. But then the servant stepped in and took the full force of the attack."