Digital Light Synthesis (DLS) technology creates ample opportunities for making 3D printed soft polymers for a wide range of grades and properties. In DLS, a 3D printer uses a continuous building technique in which the curing process is activated by an ultra-violet (UV) light. In this contribution, EUP40, a recently invented commercially available elastomeric polyurethane (EPU) printed by the DLS technology, is experimentally characterized. For characterizing the mechanical properties, an extensive viscoelastic experimental study on the digitally printed EPU taking the strain rate-dependence are conducted. The study reveals a significant time-dependency on its mechanical responses. Moreover, the material demonstrates noticeable nonlinear viscosities that depend on strain and strain rates. Based on the experimental findings for the printed elastomer, a large strain viscoelastic model is devised where evolution laws are enhanced by strain and strain rate-dependent nonlinear viscosities. Following identifications of relevant material parameters, we validate the model with the experimental data that show its good predictability. Such an extensive experimental study along with a constitutive model will help in designing and simulating more complex cellular and structured metamaterials using 3D printed elastomeric polyurethanes.