In this manuscript, we are interested in the study and numerical simulation of mechanical systems composed of interacting solids: passive or active suspensions, or granular media. The first chapter describes some of the problems raised by the study of these systems. We then focus on the numerical simulation of suspensions. This requires the resolu- tion of a coupled problem between the Stokes fluid and the rigid structures. In the second chapter, we aim to solve precisely the problem when the particles are close. The method we propose is based on an explicit asymptotic expansion of the solution when the inter-particle distance goes to zero. In the third chapter, we focus on the use of boundary element methods to solve the fluid-structure problem. We deal, in the case of Stokes equations, with the two classical difficulties for these methods: on the one hand, the development of fast algorithms to solve full systems and on the other hand, the computation of singular integrals involved in the problem. In the fourth chapter, we are interested in designing algorithms to deal with contacts (with or without friction) in the systems we consider. The algorithms described are Contact Dynamics algorithms. At each time step, the contact forces are computed in an implicit way, as solution to a convex optimization problem. Rheological studies of granular materials based on these algorithms are presented. Finally, in the fifth chapter, we study micro-swimmers evolving in a Stokes fluid. We investigate whether these swimmers can swim, that is, perform cyclic deformations (a stroke) generating a given displacement. We propose a general framework to answer this question by rewriting the problem as a control problem.