We present a special class of mechanical systems that could be written as Chua circuits with discontinuities. We recall the general frame for the study of such models. Results of existence and uniqueness are given. Then numerical results obtained via piecewise analytical expressions are presented. We discuss some bifurcation diagrams, phase portraits. Chaos is characterized by computing Lyapunov exponents. We analyze the global behavior in a special case where discontinuity stabilizes the trivial equilibrium solution.