Establishing the absence of deadlocks is important in many applications of formal methods. The use of model checking for finding deadlocks in formal models is often limited. In this paper we propose a constraint-based approach to finding deadlocks employing the ProB constraint solver. We present the general technique, as well as various improvements that had to be performed on ProB's Prolog kernel, such as reification of membership and arithmetic constraints. This work was guided by an industrial case study, where a team from Bosch was modeling a cruise control system. Within this case study, ProB was able to quickly find counter examples to very large deadlock-freedom constraints. In the paper, we also present other successful applications of this new technique. Experiments using SAT and SMT solvers on these constraints were thus far unsuccessful.