Polymers have more complicated properties since they display both elastic and viscous type responses at different strain rates. As the application of polymers increase, a thorough understanding of the mechanical behavior of these materials becomes vital in order to perform innovative and economical designs of various components. The main objective of this paper is to develop an effective method with the use of Laplace integral transform to describe the creep and relaxation properties of viscoelastic polymers. This general approach is on the basis of the integral constitutive functions for viscoelastic polymers, avoiding the use of differential stress-strain relations. Using this method, the time domain stress-stain relation can be easily obtained. As its application, the creep and relaxation properties of the materials are exhibited in the numerical examples.