In this thesis we analyse an interaction problem between two elastic three-dimensional bodies of which one is much thinner than the other. Furthermore, the thin body is assumed to be more stiff with elastic coefficients related to the small thickness parameter. We consider this problem in context of both linear and nonlinear elasticity. We analyse asymptotic behaviour of solutions of these problems and obtain different limit models in various regimes as thickness tends to zero. Furthermore, we propose both linear and nonlinear models given by three-dimensional elasticity equations and two–dimensional elastic plate equations as a boundary condition instead of the three–dimensional body equations that includes the thin body and investigate the asymptotic behaviour of the proposed model as the thickness parameter goes to zero. We prove that proposed model has the same asymptotic behaviour as firstly observed three–dimensional model that includes the thin body in the same regimes. By using proposed models, one can avoid numerical challenges that implementing a scheme for a three–dimensional model including a thin domain can cause as in similar situations. The nonlinear model we propose is based on a nonlinear shell model we formulate and it is an additional contribution of the thesis. It is a nonlinear shell model of Naghdi type defined for shells which allow Lipschitz–continuous parametrizations of its middle surface, so it also models shells with middle surfaces having corners and folded plates and shells. Energy of the formulated model contains membrane, shear, drill and flexural terms, and (in appropriate regimes) it has the same asymptotic behaviour as models rigorously justified in the literature: membrane shell model, flexural shell model and constrained membrane plate model.