In this paper we are studying the application of techniques to solve constraint satisfaction problems (CSP) for designing mechanical systems. After presenting the CSP method and the several ways to solve it, we introduce an optimization point of view for CSP. Then, we propose a quick overview of CSP application in product engineering. An example in mechanical system optimization is given via the case study of the optimal design of a bolt coupling. The case is modelled as a Constraint Satisfaction Problem on real variables. Finally, numerical results illustrate the resolution process with a CSP approach.