Boundary element method is used in this thesis to investigate mechanical response in robot grasping. Specifically, the contact size and traction distribution are determined for given tightening displacements. Contact analysis is performed be imposing the two criterions: nodes outside the contact zone do not penetrate the other body; and all tractions inside the contact zone are compressive. Numerical results are first checked against analytic results. Cases treated in this thesis include cylindrical objects grasped by rigid fingers, and rectangular elastic objects grasped by rigid or elastic fingers. The latter is performed by multiple region analysis. The dependence of contact traction on tightening displacements, on modulus of elasticity, and on finger width is discussed in this thesis.