Abstract : The work described in this thesis is a mathematical and numerical study tools to simulate the dynamics of complex nonlinear structures, quasi-incompressible, and has two characteristic length scales. To more specific about this last point, the structures considered are assumed to contain fine geometric details on their board. This study, conducted in partnership with the French Manufacturer of Tyres Michelin is largely motivated by the importance of dynamic calculations in the tire rolling to predict the value of different physical quantities: the constraints materials, ground contact pressure or acoustic radiation. In this context, difficulties in obtaining complete and realistic simulation for cost calculation are reasonably related to the complexity of the geometry, material behavior, the method of solicitation contact, or the intervention of different scales length, time or stiffness characteristics of the structure. After a description of the anatomy of the tire, we mention some issues of numerical simulation in the design phase. Then we underline the intrinsic properties of the structure that make these studies difficult. Finally, we delimit the issues that occupy the rest of this paper and outline the approach adopted. Reference is made to the content of chapters and contributions.