Cohesive cavities often occur in the solid missile motor grain. The strain field analysis of the cohesive cavity is an important problem to the evaluation of grain structural integrity. In this paper, a method to analyze the cohesive cavity's strain field is presented. With accelerated aging test, the variation law of the extensibility of propellant in the storage period was obtained. Using three-dimension viscoelastic finite element method, the Von Mises strain of the grain with cohesive cavities under internal pressure and axial acceleration loading was analyzed. In comparing the extensibility of propellant and the Von Mises strain of the grain in different storage period, the allowable maximum diameter of the cohesive cavity in different storage period was determined by the maximum Von Mises strain criterion. The analysis of a practical motor shows that the analytical method and these conclusions are available for using solid motor with cohesive cavities.