This thesis deals with the nonlinear analysis of stability loss of flue gas pipe. This pipe is a part of desulphurization line. The thesis describes the creating of a simplified FEM model. It also describes the setting of the boundary conditions of the model for few loading cases. These cases differ by preference for one of the load as dominant. There are proposed several variants of stiffening by light ring stiffener. The work is finished by comparing the resistance to the stability loss of the reinforced variants and unreinforced model of flue gas pipe.