In this paper we extend the range of applicability of the boundary element method (BEM) for concentrated elastic contact problems by computing the influence coefficients (ICs) numerically. These ICs represent the Green's function of the problem, i.e. the surface deformation due to unit loads. For the half-space they are analytically available. An elastic model is proposed to compute these coefficients numerically, by the finite element method (FEM). We recommend proper strategies of FEM meshing and element types, considering accuracy and computational cost. The effects of computed ICs to contact solutions are examined for a Cattaneo shift problem. The work in this paper aims at providing a reference to study fast solvers for the conformal contact problem where ICs are not analytically known.