  We use the method of Faltings (Arakelov, Par\v{s}in, Szpiro) in order to
explicitly study integral points on a class of varieties over $\mathbb Z$
called Hilbert moduli schemes. For instance, integral models of Hilbert modular
varieties are classical examples of Hilbert moduli schemes. Our main result
gives explicit upper bounds for the height and the number of integral points on
Hilbert moduli schemes.
