The present study submits a mixed finite element model to solve atransient thermoelastic contact of non-conformal deformable bodies.The model is concerned with the coupled quasistatic class ofthermoelasticity in which the inertia term is discarded. Attention iscentered on homogeneous and isotropic materials whose thermal andelastic properties do not depend on the temperature.The nature of the problem depends strongly on the direction of heatflow and the value of distortivity of the two bodies. This model can beused for the case of heat flows into the material with larger distortivity.The solution’ procedure consists of two simultaneous variationalmodels. The first one concerns with the transient heat transfer problembetween the two contacting bodies considering the conventional thermalboundary conditions at the contact interface. The direct integrationmethod is used to discrete the time domain of that model. The secondmodel is used next to invistigate the multila~ered s~stemsinclude the triangular laminated plates with apex angle andthe skew laminated plates. The results include elongations,X-traction and shear stress. The results provide newinsight into the ph~sics as well as the computationalaspects of the elasto-plastic multila~ered s~stems.