The authors consider a finite set of rigid bodies connected partly bilaterally and partly by means of punctual contacts with each other. At the contact points dry friction is assumed to be present and unilateral conditions hold there. The dynamical behaviour of the system is studied rather generally using concepts of modern functional analysis including variational inequalities and subdifferentials. After the mathematical formulation of the problem and basic assumptions existence theorems are given. Then the mechanical equations and constraints are discussed particularly, followed by the proofs of the theorems. As an illustration the authors analyse a two body system with one degree of freedom and show that shocks may occur.