The strong radial gradients that exist in the plasma edge (scrape-off layer and divertor) of tokamaks increase the magnitude of some previously neglected viscous terms to the same order as the other terms traditionally included in fluid plasma transport calculations. The standard fluid equations are modified to include these new viscous force and heat flux terms that are important in the plasma edge. These new terms give rise to viscous-driven radial particle and energy fluxes that are estimated to cause an order unity reduction in the radial peaking of energy fluxes incident on divertor collector platesy thus illustrating the importance of taking them into account in fluid calculations of divertor operation. A viscous drift velocity is found to be comparable in magnitude to the standard E × B and pressure gradient-driven drift velocities. The modified fluid equations are formulated to facilitate the inclusion of these important new viscous terms into fluid transport codes used for tokamak edge modeling.