We define a notion of model for the $\lambda \Pi$-calculus modulo theory, a notion of super-consistent theory, and prove that proof-reduction terminates in the $\lambda \Pi$-calculus modulo a super-consistent theory. We prove this way the termination of proof-reduction in two theories in the $\lambda \Pi$-calculus modulo theory, and their consistency: an embedding of Simple type theory and an embedding of the Calculus of constructions.