Polymers have been proved to have attractive mechanical characteristics, which made it desirable to choose these materials over traditional materials for numerous types of applications. As the uses 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 the Laplace inverse transform to describe the time dependent mechanical response of viscoelastic polymers. This general methodology is based on differential constitutive relations for viscoelastic polymers, avoiding the use of relaxation integral functions. As its application, the creep and relaxation properties of the materials are exhibited in the numerical examples.