The quoted excerpt from Isaiah 53 above 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 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 previously referenced passages from the New Testament are based on the vicarious nature of the atonement 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 were an innocent substitute. Though animal sacrifices temporarily stayed the judgement of God, the Levitical sacrificial system pointed to the perfect, once for all 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 Traslatio 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."
The following excerpt was taken from a study by William D. Barrick, Professor of Old Testament:
"The Septuagint (LXX) evidences a pre-Christian Jewish understanding of atonement (especially in the use of the Hebrew words for atonement, 19 [kipper) and 19 [koper]) as propitiation since it employs é u dokopci (exilaskonal) 83 times for translating kipper." Summing up a detailed analysis, Morris deduces that the basic meanings of kipper and ĆELA.COkouci involve the thought of the offering of a ransom which turns away the divine wrath from the sinner." In addition to ransom and divine wrath, kipper "denotes a substitutionary process... so plain as to need no comment in the cases where life is substituted for life. Since the OT reveals the reality of divine wrath, it cannot be ignored or explained away as impersonal wrath, mild displeasure, mere irritation, or capricious passion. In nearly 600 OT texts more than 20 different Hebrew words provide a rich wrath vocabulary. Divine righteousness, holiness, and justice require divine retribution. Without divine retribution, divine mercy becomes nothing more than a vestigial appendage without function or purpose."
Jewish scholar Herz Homberg recognized Isaiah 53 as a Messianic prophecy and gave this commentary in his exposition of the entire Old Testament called Koren:
"The fact is that it refers to the King Messiah, who will come in the latter days, when it will be the Lord’s good pleasure to redeem Israel from among the different nations of the earth…and even the Israelites themselves will only regard him as ‘one of the vain fellows’, believing none of the announcements which will be made by him in God’s name, but being contumacious against him, and averring that all the reproaches and persecutions which fall to his lot are sent from heaven, for that he is ‘smitten of God’ for his own sin. The fact is, that it refers to the King Messiah, who will come in the latter days, when it will be the Lord’s good pleasure to redeem Israel from among the different nations of the earth…..Whatever he underwent was in consequence of their own transgression, the Lord having chosen him to be a trespass-offering, like the scape-goat which bore all the iniquities of the house of Israel."