This paper presents a method for simulating anisotropic friction for deforming surfaces and solids. Frictional contact is a complex phenomenon that fuels research in mechanical engineering, computational contact mechanics, composite material design and rigid body dynamics, to name just a few. Many real-world materials have anisotropic surface properties. As an example, most textiles exhibit direction-dependent frictional behavior, but despite its tremendous impact on visual appearance, only simple isotropic models have been considered for cloth and solid simulation so far. In this work, we propose a simple, application-oriented but physically sound model that extends existing methods to account for anisotropic friction. The sliding properties of surfaces are encoded in friction tensors, which allows us to model frictional resistance freely along arbitrary directions. We also consider heterogeneous and asymmetric surface roughness and demonstrate the increased simulation quality on a number of two- and three-dimensional examples. Our method is computationally efficient and can easily be integrated into existing systems.