A numerical method is developed to compute the pressure distribution and normal approach in a generalized elliptical contact between layered linearly elastic solids. The computed quantities are obtained as an approximate solution to an integral equation formulated for the most general case of Hertzs assumptions, i.e., the frictionless contact between arbitrary surfaces whose undeformed normal separation can be approximated by the separation between an elliptical paraboloid and the tangent plane at its vertex. The numerical method is based on a discretized representation of the unknown pressure distribution. The method is applied to the contact between a homogeneous solid and a layered solid consisting of an isotropic surface layer of uniform thickness in perfect adhesian to an isotropic substrate. Comparisons with available solutions for the limiting cases of Hertz contact between homogeneous solids and axisymmetric contact of layered solids establish the accuracy of the numerical method.