I would avoid using the language of “Mass” and concentrate rather on the idea of “liturgy”.
Here is what Vatican II’s Constitution on the Sacred Liturgy said about this:
7. …] Rightly, then,
the liturgy is considered as an exercise of the priestly office of Jesus Christ. In the liturgy
the sanctification of the man is signified by signs perceptible to the senses,
and is effected in a way which corresponds with each of these signs; in the liturgy
the whole public worship is performed by the Mystical Body of Jesus Christ, that is, by the Head and His members.
Let’s look at each of those bolded parts:
The liturgy is considered as an exercise of the priestly office of Jesus Christ. Jesus, because He is the true and ultimate Messiah (Christ), is anointed as high priest, prophet, and king. The liturgy is an exercise of Jesus’ capacity as high priest. It is worship offered to God the Father.
In the liturgy the sanctification of the man is signified [and] effected. After the second coming, there will be no need for man to be sanctified. God will be all in all, those in Heaven are already sanctified. So I would suspect that this particular end of the liturgy would not continue in Heaven.
In the liturgy the whole public worship is performed by the Mystical Body. The liturgy, while an exercise of Christ’s priestly office, is performed not only by Christ (the Head) but also by His members (the Body).
- In the earthly liturgy we take part in a foretaste of that heavenly liturgy which is celebrated in the holy city of Jerusalem [Rev 21:2] toward which we journey as pilgrims [Phil 3:20], where Christ is sitting at the right hand of God [Col 3:1], a minister of the holies and of the true tabernacle [Heb 8:2]; we sing a hymn to the Lord’s glory with all the warriors of the heavenly army [Isa 6:3; Rev 4:8]; venerating the memory of the saints, we hope for some part and fellowship with them [cf. Roman Canon, *Nobis quoque]; we eagerly await the Savior, Our Lord Jesus Christ [Phil 3:20], until He, our life, shall appear and we too will appear with Him in glory. [Col 3:4]
This paragraph explicitly addresses the unity of the earthly liturgy and the heavenly liturgy. There are a few resonances with the book of Revelation in the paragraph, namely the “holy city of Jerusalem” (i.e. the Church, the bride of the Lamb who is Christ) and the hymn of the angels, “Holy, holy, holy!” The book of Revelation gives us an insight into the liturgy of Heaven. I do not think we can say the “holy sacrifice of the Mass” goes on in Heaven, but that the holy sacrifice of the Mass on earth is our participation in what is happening in the heavenly liturgy.
I would describe the heavenly liturgy this way: Christ, the Lamb who was slain but stands (Rev. 5:6), offers Himself to the Father, and through and around this offering, all the saints and angels give glory and praise and honor and worship to the Father.