Abstract. This article presents several related methods for drawing traces. First, it is shown how to draw traces uniformly at random in large models composed of several components. Then a method for drawing traces according to a given coverage criterion is presented, together with a notion of randomised coverage satisfaction. These methods rely on combinatorial algorithms, based on a representation of the model by an automaton or by a product of several automata, synchronised or not. We report several experimental results on random generation of traces in large transition systems, and on statistical testing of C programs.