A configurational bias Monte Carlo method has been developed to study the static friction between grafted polymers immersed in a good solvent. Simple models using the soft quadratic potential from a dissipative particle dynamics study have been used to model polyzwitterionic brushes at physiological pressures (up to 7.5 MPa). Three models of decreasing rigidity have been used to model the friction between the brushes by calculating the tangential component of the pressure induced by a mismatch in the registry of the two grafting surfaces. The static friction coefficient can be calculated for three model systems and the slip between the layers occurs at a much lower values of shear force for the more flexible polymer layer. A moderate increase in the flexibility of the chains reduces the friction coefficient by a factor of ca. 20. Tilting the layer directors of the brushes also increases the static friction between the layer when the top, tilted layer is displaced in the direction away from the tilt. Non-equilibrium dynamics techniques for the same model were performed using dissipative particle dynamics and the limiting extremes of the Stribeck curve corresponding to the boundary lubrication regime and the hydrodynamic lubrication regime were observed for these flat surfaces. As expected, mu(k) is significantly lower than mu(s) for the same system. The dynamical friction coefficients in the model are in good agreement with those observed in the experiment and the ratio of mu(k)/mu(s) of between 0.11 and 0.5 observed in the simulations is in reasonable agreement with the value of 0.5 normally observed for these seen for these systems.