Abstract: A kind of three-dimension viscoelastic perturbation stochastic finite element method (VPSFEM) was developed, and then the VPSFEM method was applied in the stochastic analysis of solid rocket motor grains. Based on the incompressible and nearly incompressible viscoelastic finite element methods, uncertainties associated with structural parameters were dealt with using the first-order stochastic perturbation technique, and recursive formulations of viscoelastic perturbation stochastic finite element method were derived. The method for evaluating statistical characters of structural responses was also presented. The randomness of solid propellant mechanics properties and loads was taken into account in the derivation. The 3D stochastic analysis of solid rocket motor grain under typical loads was performed. The simulated results show that the 3D viscoelastic perturbation stochastic finite element method is efficient, and its accuracy can meet the requirement of engineering projects.