We consider finite size effects on calculation of the viscosity of bulk molecular fluids using molecular dynamics simulations. The results are obtained using equilibrium simulations, direct calculations from nonequilibrium molecular dynamics simulations and calculations of the transient time correlation function expression, based on the dissipation theorem for nonlinear response. As with atomic fluids, strain induced by the periodic boundary conditions on the molecular systems can become significant for small systems at high densities and low temperatures. It addition to this effect, the dissipation function has a finite size contribution below a critical size, and this becomes more important as the system size is reduced and the length of the molecule increases. In this paper we show how calculations can be carried out to obtain convergence to bulk values with limited system size simulations.