Considerable progress have been done since 25 years on the thermomechanical modeling of the lithospheric strain and stress. Since the first numerical models, the central question has been to elucidate the relationship between the forces that load the lithosphere, the lithospheric rheology and the strain observed at the surface and within the crust. Due to the complexity of the physical problem and because of the limited power processing, strong simplifications have been made. The first goal of the talk will be to review the advances that have been made in different directions:

• the lithospheric rheology, which has evolved from averaged viscous laws to layered stratification such aspredicted by experimental rock rheology;
• the geometrical model complexity, which allows now to precisely account for the structural lithospheric properties and for complex boundary conditions;
• the treatment of the localization of the deformation;
• the incorporation of erosional processes for collisional belts.

The second part of the talk will be devoted to discuss some open problems. The first one is the lithosphere-asthenosphere coupling, which is not achieved. Completing this task is essential as it should allow to solve the problem of forces responsible of plate tectonic. The second one is the apparent weakness of large faults, which is not compatible with rock mechanics insights. How can we use mechanical modeling to resolve this paradox ?