In this work, a new generalized non-Euclidean friction law is proposed. This friction law allows the friction coefficients in the tangential and axial directions of the roll to be different. A three-dimensional, large-strain, non-steady state elastic-plastic finite element analysis has been performed for the flat rolling process. The contact and friction problem at the interface between the workpiece and the rolls is treated rigorously. The finite element procedures are based on the updated Lagrangian virtual work equations in incremental form. The solution at each time step is accepted only if the equilibrium of nodal forces, the calculation of which is an exact treatment, is reached pointwise. The numerical results, including the interfacial normal and shear stresses, are presented and discussed.