SUMMARYBased on the weighted residual technique, both Finite Element and Boundary Element alternative procedures for viscoelastic analysis are proposed. After imposing the space approximations, applying the kinematical relations for material and strain velocities at the approximation level, the time integration is carried out using appropriate operators. The Kelvin-Voigt viscoelastic model is implemented in order to validate the idea. The Newmark ÿ time integral scheme is applied to the Finite Element procedure while the Houbolt scheme is applied to the Boundary Elements, allowing the consideration of dynamic analysis in future works.