Objection 1. It would seem unfitting for Christ to have been buried, because it is said of Him (Psalm 87:6): "He is [Vulgate: 'I am'] become as a man without help, free among the dead." But the bodies of the dead are enclosed in a tomb; which seems contrary to liberty. Therefore it does not seem fitting for Christ to have been buried.
Objection 2. Further, nothing should be done to Christ except it was helpful to our salvation. But Christ's burial seems in no way to be conducive to our salvation. Therefore, it was not fitting for Him to be buried.
Objection 3. Further, it seems out of place for God who is above the high heavens to be laid in the earth. But what befalls the dead body of Christ is attributed to God by reason of the union. Therefore it appears to be unbecoming for Christ to be buried.
On the contrary, our Lord said (Matthew 26:10) of the woman who anointed Him: "She has wrought a good work upon Me," and then He added (Matthew 26:12)--"for she, in pouring this ointment upon My body, hath done it for My burial."
I answer that, It was fitting for Christ to be buried. First of all, to establish the truth of His death; for no one is laid in the grave unless there be certainty of death. Hence we read (Mark 15:44-45), that Pilate by diligent inquiry assured himself of Christ's death before granting leave for His burial. Secondly, because by Christ's rising from the grave, to them who are in the grave, hope is given of rising again through Him, according to John 5:25-28: "All that are in their graves shall hear the voice of the Son of God... and they that hear shall live." Thirdly, as an example to them who dying spiritually to their sins are hidden away "from the disturbance of men" (Psalm 30:21). Hence it is said (Colossians 3:3): "You are dead, and your life is hid with Christ in God." Wherefore the baptized likewise who through Christ's death die to sins, are as it were buried with Christ by immersion, according to Romans 6:4: "We are buried together with Christ by baptism into death."
Reply to Objection 1. Though buried, Christ proved Himself "free among the dead": since, although imprisoned in the tomb, He could not be hindered from going forth by rising again.
Reply to Objection 2. As Christ's death wrought our salvation, so likewise did His burial. Hence Jerome says (Super Marc. xiv): "By Christ's burial we rise again"; and on Isaiah 53:9: "He shall give the ungodly for His burial," a gloss says: "He shall give to God and the Father the Gentiles who were without godliness, because He purchased them by His death and burial."
Reply to Objection 3. As is said in a discourse made at the Council of Ephesus [P. iii, cap. 9, "Nothing that saves man is derogatory to God; showing Him to be not passible, but merciful": and in another discourse of the same Council [P. iii, cap. 10]: "God does not repute anything as an injury which is an occasion of men's salvation. Thus thou shalt not deem God's Nature to be so vile, as though It may sometimes be subjected to injuries."
Source: Summa Theologica (New Advent)