Mathematical model for surface bending

The paper investigates the mathematical model of infinitesimal bendings of the surface. This model is a system of Cauchy-Riemann equations, which allows exploring these deformations for the surfaces of positive curvature. In the case of an elliptic paraboloid is a vector of such deformations by analytical method as a solution of the Riemann-Hilbert problem with time - discontinuous boundary conditions for the Cauchy-Riemann equations. A numerical analysis of the resulting mathematical model at various specified boundary conditions is carried out.