A numerical method for solving contact problems is developed and then used to predict friction (without adhesion) between rubber in plane strain and periodic arrays of parabolic and triangular substrate asperities; the numerical method itself, which is based on the fast Fourier transform algorithm, is not limited to these asperity shapes. Also, effects of superposing two and more scales of texture are described. Some generalizations and related applications, such as analysis of tire traction, are then discussed.