The system composed of a face covering layer + spatially locally curved substrate reinforcing layer + half-space is taken into consideration. It is presumed that this framework is compressed at infinity by uniformly distributed normal forces and it is required to establish the self-equilibrated normal stresses in that, caused by locally curved of the substrate reinforcing layer. The matching boundary and contact value problem is defined within the scope of 3-D geometrically non-linear exact equations. Formulated problem's solution is introduced with the series form of small parameter which represents the degree of the aforesaid locally curving. These series' zeroth and first approximation are ascertained with the utilization of double Fourier transform. The original of values that are searching is ascertained numerically. Corresponding numerical outcomes about the self-equilibrated normal stress caused by this spatially local curving are presented and discussed.