A steady state simulation for the flow past a circular cylinder at the sub-critical Reynolds number of 3900 is conducted using a variety of non-linear eddy viscosity-based two-equation κ-ε models. Although, this simulation compromises the transient characteristics of the flow, the solution obtained using a steady state simulation showed qualitative relevance. Steady state results were closely comparable to the far more expensive and supposedly more correct time-averaged solutions obtained using transient simulations. The dissipative effect due to such turbulence modeling by far overweighs the effect of the numerical dissipation. Such dissipation dampened the intrinsic self-excited unsteadiness known to exist in such flow and enabled steady state-like solution. In-house developed finite volume based code along with a commercial finite-element code, were used. Qualitative agreement is attainable for the surface-pressure distribution over the cylinder and the centerline streamwise velocity in the wake regions. For this type of problems, the time-averaged solutions obtained using transient simulation that employs the non-linear eddy viscosity-based two-equation κ-ε type models, offered marginal improvement over those obtained using steady state simulations.