A new finite element technique for the numerical simulation of 3D time-dependent flow of viscoelastic fluid is presented. The technique is based on a Lagrangian kinematics description of the fluid flow. It represents a further development of the 3D Lagrangian integral method (3D-LIM) from a Rivlin-Sawyers fluid to a fluid described by a generalized molecular stress function (MSF) model allowing the use of dissipative convective constraint release in the constitutive equation. The convergence of the method is demonstrated on the axis-symmetric problem of the inflation of a polymeric membrane only restricted by a clamping ring.