Abstract : Equations of motion for viscoelastic fluids are non linear PDE's well studied in literature specially by the engineers. However, many mathematical questions for these equations are yet to be resolved in complete details. Stochastic models and control problems for these equations are wide open questions too. In this talk I will investigate the system of stochastic partial differential equations perturbed by L\'{e}vy noise, describing the motions of such fluids. The viscoelastic and inviscid elastic models will be discussed separately. Exploiting monotonicity argument I will establish the existence of unique stochastic strong solutions in suitable spaces for both the cases.