  We construct integral models for moduli spaces of shtukas with deep
Bruhat-Tits level structures. We embed the moduli space of global shtukas for a
deep Bruhat-Tits group scheme into the limit of the moduli spaces of shtukas
for all associated parahoric group schemes. Its schematic image defines an
integral model of the moduli space of shtukas with deep Bruhat-Tits level with
favourable properties: They admit proper, surjective and generically \'etale
level maps as well as a natural Newton stratification. In the Drinfeld case,
this general construction of integral models recovers the moduli space of
Drinfeld shtukas with Drinfeld level structures.
