With regard to the analysis of the stress-strain state of the flange connection node GRP pipes under internal pressure and the clamping force tasked with the linear theory of viscoelasticity piecewise homogeneous orthotropic materials. A variant of iterative method for solving the problem using the finite element method. As a result of numerical studies of regularities of evolution of a busy site conditions, in particular the relaxation of tightening force. A starting value of tightening efforts, providing long-term tightness of the connection.