Abstract: Since solid propellant exhibit nearly-incompressible material behaviour,the displacement formulation of the finite element method is unable to give acceptable solution to mechanical problems of these materials.This paper introduces a new constitutive relation based on Herrmann variational theorem for incompressible and nearly-incompressible viscoelasticity.The corresponding finite element formulation is presented here and a computer program VFAPINP is developed for solution to plane problems.The results show that the approach and the computer program are valid for stress analysis of viscoelastic materials with all admissible values of Poisson′s ratio and particularly for the propellant grain stress analysis.