The plane problem of nonlinear elasticity (the plane strains) has been considered for bi-material plane under the action of a concentrated force on the interface. Mechanical properties of half-planes are described by the model of John's harmonic material. Application of this model has allowed to use the methods of theory complex functions and receive exact analytical solution of problem. The values of nominal stresses, Cauchy stresses and displacements have been found in a point of application of force. As a special case of the problem of concentrated force in a bi-material plane, the solution of the problem of concentrated force at the boundary of the half-plane is obtained for John's material model. The asymptotics of the stresses and displacements have been constructed in the vicinity of point of application of force from the exact solutions.