This work presents a characterization of the influence of viscoelasticity on the mechanical behavior of bovine pulmonary arteries. It is commonly accepted that biological soft tissues do indeed exhibit viscoelastic characteristics; however its effect has yet to be quantified. Stress relaxation tests are used to determine the time dependent response of bovine pulmonary tissue. Fitting this data to a modified standard linear solid model, allows a total of five independent time constants are attained, each of which describe individual time scales on which the medium has a viscoelastic response to an applied strain. These time constants are applied to an analytical model through the Boltzmann integral in order to describe the stress response to a prescribed loading strain. The strain used in this case was a sine wave in order to mimic the in vivo flow of blood from the heart. These results were also modeled using finite element simulations in order to verify the time dependent response. It was found that although viscoelasticity is a necessary consideration, depending on the loading conditions, it may in some cases be either neglected or simplified. A time scale at which testing should be done in order to reduce time dependent effects as well as a simplified model describing the viscoelastic effect on the ultimate tissue response is presented.