Viscoelastic behavior is frequently observed in dynamical flexible multibody systems. In the simplest form it is manifested in one dimensional revolute and prismatic joints. Beyond which more complex force elements such as six degree of freedom flexible joints can also be found. Finally, beams, plates and shells are found to exhibit viscoelastic behavior too. In the past extensive work has been done on analyzing the dynamic response of three dimensional beams by performing cross-sectional analysis through finite element methods and subsequently solving the reduced beam problem. The approach is particularly relevant for the analysis of complex cross sections and helps improve computational efficiency significantly. A formulation which incorporates a viscoelastic model of the generalized Maxwell type with a solution of the three dimensional beam theory which gives an exact solution of static three dimensional elasticity problems is presented. Multiple examples incorporating the use of the aforementioned model in the context of viscoelastic beams and joints are presented. Shortcomings of the Kelvin-Voigt model, which is often used for flexible multibody systems, are underlined.