There are several models for understanding the nature of the atonement. Some see the atonement as a ransom of sinners by Christ. The theory of “Christus Victor” (Victorious Christ) holds that Jesus defeated the evil cosmic powers and freed his people from their control. In the middle ages, Anselm popularized the satisfaction theory. Briefly, this position says that sin dishonors God by denying him what is inherently his. Man renders an infinite offense to God's majesty and satisfaction is required by him. This satisfaction is met in Christ's atoning work.
There is merit in each of the views of atonement, but the penal nature of atonement is unavoidable in the Scriptures and it is one key reason for Jesus’ incarnation. In fact, I believe that the penal substitutionary theory of atonement, in a way, undergirds all the other theories. I do not believe we should limit ourselves to one model of atonement. The work of God through Christ in the atonement is so great that many of the theories provide illumination upon a different facet of God’s wondrous work.
Penal substitutionary atonement refers to the divine punishment for sin being inflicted upon the body of Christ instead of on the guilty sinner deserving of that punishment. For most of history, this was understood to be a Bible truth, although it was underlying some other atonement theories. Many have rejected penal substitutionary atonement because it points to the demand that God actually punishes sin in order to remain just. Many believe they are too enlightened to believe in a God who would demand actual punishment for sin.
Penal substitutionary atonement is seen in passages which describe Jesus “bearing the sin of many” (Is. 53:12) and being the one upon whom the Lord “has laid the iniquity of us all” (Is. 53:11). 1 Peter 2:24 says, "He himself bore our sins in his body on the tree, so that, having died to sins, we might live to righteousness. By his wounds, you have been healed.” The Bible teaches: “The sacrifice is both provided by God and offered to God; God offers himself in the gift of his Son to achieve a just and merciful forgiveness of sinners. It is God himself who makes the complete sacrifice.”
Hebrews 10 argues for the atonement being possible because of the physical body of Christ. The blood of the spotless Lamb of God was able to take away sins once and for all (Hebrews 10:4). The nature of the atonement inherently demands punishment of sin. Isaiah 53:10-12 presents both the suffering and the reward of the Savior. Peter wrote, “he himself bore our sins in his body on the tree, that we might die to sin and live to righteousness. By his wounds you have been healed” (1 Peter 2:24).
The physical body of Christ enabled the eternal Word to accomplish salvation on our behalf. Christ, in his physical body, died on our behalf (Romans 8:32; 14:15; 1 Corinthians 8:11; Galatians 2:20). Christ died for our sins (Romans 5:6, 8; Galatians 1:3-4). Jesus likewise spoke of himself as the definitive, all-powerful, and foundational sacrifice. Because of the physical body and blood, Jesus said, “This is my blood of the covenant, which is poured out for many” as he instituted the Lord’s Supper (Mark 14:24). These words alluded to the physical sacrifice of Exodus 24:8, “And Moses took the blood and threw it on the people and said, “’Behold the blood of the covenant that the Lord has made with you in accordance with all these words.’” Jesus was the perfect and final physical sacrifice for sin and sinners.
Hebrews 9 also points to the necessity of a perfect and heavenly sacrifice which will bring about true atonement. The necessity of the divine Word’s incarnation is presented in Jesus’ spiritual entrance into the heavenly temple (Heb. 9:24), and Jesus’ offering of his physical blood as a physical sacrifice (Heb. 9:25-26). The atonement encapsulates the work of Christ as the ransom (Mark 10:45); sacrifice (Hebrews 10:11-14); reconciliation (Ephesians 2:16); victory (Colossians 2:13-15); and the regaining of what was lost by Adam (Romans 5:12-21). Christ is our High Priest who offers atonement for our sins (Hebrews 2:17; Romans 3:25; 1 John 2:2). He is the glorious Savior who should be praised
J. I. Packer eloquently described the atoning work of Christ when he wrote:
If the true measure of love is how low it stoops to help, and how much in its humility it is ready to do and bear then it may be fairly claimed that the penal substitution model embodies a richer witness to divine love than any other model of atonement, for it sees the Son at the Father’s will going lower than the other views suggest.
The penal nature of the atonement is not for a lack of God’s love. Rather, it is the greatest demonstration of love God could manifest.
 J. I. Packer and Mark Dever. In My Place Condemned He Stood (Wheaton: Crossway, 2007): 94.