Current theories to describe friction of glaciers over hard beds are formulated on the basis that ice is free of debris and slides perfectly over the glacier bed. However, it is common to find basal layers of debris-laden ice or frozen patches that could exert additional resistance to glacier flow. We provide an analytical solution that accounts for the effect of solid friction in the framework of Weertman (1957). The presence of solid friction slows glacier sliding, however not as much as expected due to a decrease in basal ice viscosity. This arises because of the mechanical feedback that tangential stress has on the ice viscosity. We further study this problem under the added complexity of cavity formation using a numerical finite element model of glacier sliding over a sinusoidal bed under steady-state conditions. The law with solid friction retains the overall shape of the pure-sliding friction law, including the rate-weakening regime, and most of the changes can be explained via the modification of the scaling parameters of the friction law with the previously derived solutions. Finally, we provide parameterizations of glacier sliding with friction to be used in large scale flow models.