The migration of tumor cells is a key aspect of extravasation, when cancer cells exit the capillaries and enter organs. Notwithstanding the relevance to understand the degradation dynamics, the elasticity of the vessel wall and the cell adhesion play a major role. The determination of the mechanical action exerted by a tumor cell on the vessel wall is a specific example of the prediction of the stress field exerted by a cell in a soft environment. In the planar case, this subject has been addressed about ten years ago by Dembo and Wang (1999). They showed how the traction exerted by a cell on a deformable substrate can be indirectly obtained on the basis of the displacement of the underlying layer. The standard approach in this respect is to solve exactly the elasticity problem by Green functions and then minimize the error by discrete optimization, iteratively. One possible alternative strategy to approach this inverse problem is to exploit the adjoint elasticity equations for the substrate, obtained on the basis of the minimization requirement of a suitable functional. In this case the linear elasticity problem is solved in an approximate way, while being intrinsically coupled with the minimization algorithm. In a joint collaboration with the Grenoble University (Claude Verdier, Valentina Peschetola, Alain Duperray) this methodology has been recently applied to determine the force field generated by T24 tumor cells on a polyacrylamide substrate. The shear stress obtained by numerical integration provides quantitative insight of the traction field generated by cells of this line and is a promising tool to investigate the spatial pattern of forces generated in cell motion.