At the Memento for the Dead, a Prayer for the Catholic Mass
At the Memento for the Dead Mass Prayer
I offer Thee again, O Lord,
this holy sacrifice of the Body and Blood of Thy only Son,
in behalf of the faithful departed,
and in particular for the souls of [here name whom you chiefly propose to pray for]
my parents, [if dead] relatives, benefactors, neighbors, etc.
Likewise of such as I have any ways injured
or been the occasion of their sins;
of such as have injured me, and been my enemies;
of such as die in war, or have none to pray for them, etc.
To Thee, O Lord, and to all that rest in Christ,
grant, we beseech Thee, a place of refreshment, light, and peace:
through the same Christ our Lord.
At the Memento for the Dead is a Catholic Mass Prayer we can pray silently after the consecration of the Body and Blood of Christ when the priest prays for those who have died. We can specifically name those we know who have passed away and we can also pray for those who have died whom we do not know. We ask Christ, through His grace and sacrifice, to grant eternal refreshment, light, and peace to those who have passed away.
If you are looking for a prayer to say for someone who has passed away, you can find one here: Eternal Rest Prayer.