Analytical solutions of the nonlinear problems (plane strain) are obtained for bi-material plane and half-plane exposed to the point force. Two models of harmonic materials are considered: semi-linear and John’s. These models allow to use the methods of complex functions for the solution of the plane problems of elasticity. Expressions for nominal stresses and Cauchy stresses, as well as for current coordinates are founded. On the base of the general expressions the asymptotic expansions are constructed for stresses and displacements in a vicinity of a point force. A comparison between the singular members of stresses and displacements is made for the two models of a material. Refs 15.