In this paper, an incremental finite element model (IFEM) for the transient analysis of viscoelastic solids is developed. The viscoelastic constitutive response is modeled based on the hereditary integral. Two new incremental constitutive forms suitable for finite element implementation are derived; creep-based (CB) and relaxation-based (RB) and, as a consequent, the difficulties associated with the interconversion from the relaxation modulus to the creep compliance and vice versa are avoided. Creep compliance and relaxation modulus are, respectively, modeled using generalized Kelvin–Voigt model and generalized Wiechert’s model. To check the validity, the computational procedure, semi-analytical solution is derived for simple viscoelastic cases using Laplace and inverse Laplace transform techniques. The obtained results from the computational procedure are compared with that obtained from the derived semi-analytical solution. To show the validity and applicability of the developed model, two different applications under different excitation patterns are presented. In each application, the time response for displacements and stresses, especially for the dynamic stress concentration factor for both elastic and viscoelastic analyses are investigated. Moreover, the dissipative recoverable nature of the viscoelastic solids under different loading-unloading excitation patterns is illustrated.