In this paper we consider the problem of a curve piecewise-homogeneous rectangular plate from an isotropic material. There are two group of condition on the line of a contact: geometric conditions,describing the continuity and smoothness of midsurfase of composite plate and force conditions, which supply the equality of bending moments and generalized cutting forces in the left and in the right parts of the plate. To find a solution we suggest a modified spline-collocationmethod, according to which the nondimensional deflection of the different part of plate may be presented as a linear combination of B-splines of fifth power. These combination are selected so, that the condition on the vertical side of the plate and the condition on the contact line are fulfilled. Different types of boundary problems are presented, which are solved numerically by the method of discrete ortogonalization of Godunov.