A finite-element model of the interaction of an elastic–plastic asperity junction based on cylindrical or spherical asperities is used to predict sliding friction coefficients. The modelling differs from previous work by permitting greater asperity overlaps, enforcing an interface adhesional shear strength, and allowing material failure. The results of the modelling were also used to predict friction coefficients for a stochastic rough surface. The asperities were based on the titanium alloy Ti-6Al-4V, and the magnitudes of the predicted friction coefficients were generally representative of experimental measurements of sliding friction. The results suggest that friction arises from both plasticity and tangential interface adhesion.