One of the main goals of model-driven engineering is the manipulation of models as exclusive software artifacts. Model execution is in particular a means to substitute models for code. We focus in this paper on verifying model executions. We use a contract-based approach to specify an execution semantics for a meta-model. We show that an execution semantics is a seamless extension of a rigorous meta-model specification and is composed of complementary levels, from static element definition to dynamic elements, execution specifications as well. We use model transformation contracts for controlling the dynamic consistent evolution of a model during its execution. As an illustration, we apply our approach to UML state machines using OCL as the contract expression language.