During long-term stacking storage, creep deformation of polymeric composite directors used in multiple launch rocket system can appears, which affects rocket launch. In this work, E-glass/epoxy 6509 composite laminates were prepared and the 60/60-minute creep/creep-recovery tests were carried out in the transverse and shear directions at different stress levels. Parameters of the Schapery’s nonlinear viscoelastic equation were obtained based on the test data. Then, a three-dimensional nonlinear viscoelastic constitutive model based on Schapery’s equation was implemented in the standard finite element code UMAT and a finite element model was developed to predict the creep deformation of the composite directors after 15 years of stacking storage. The effect of creep deformation on rocket launching was also studied The results show that the residual deformation of the directors is a saddle-shaped distribution in three-dimensional space, the maximum residual deformation is 0.24 mm, and the minimum residual deformation is 0.22 mm. The creep deformation of the director causes a significant increase in the contact-collision force during launching, resulting in a decrease in the rocket run-off track velocity.