In this paper, an inverse analytical technique to obtain contact stress distributions between two elastic bodies is proposed. The technique uses a strain datum distant from the contact region. The finite-element method and the numerical optimizing technique (DFP method) are applied to formulate the method. Moreover, the formulation of strain sensitivity analysis for the DFP method is proposed. By using this inverse technique, two-dimensional contact problems are analyzed. The reasonable contact area and stress distribution are obtained from the strain datum measured experimentally. The results are compared with an inverse analytical result using isochromatics.