The mechanical behavior of fibrous assemblies, particularly the transverse behavior of fiber yarns and multifilament strands depends, inter alia, on the fiber-to-fiber contact and sliding. All studies on inter fiber friction presented in the literature focus on cases where the relative inter fiber motion occurs either in longitudinal-to-longitudinal or longitudinal-to-transverse direction. The transverse-to-transverse inter fiber friction plays an important role as far as the mechanical transverse behavior of fiber yarns and multifilament strands are concerned. In order to evaluate the case named here ‘transverse friction, the present study proposes an original method and an associated model analyzing the transversal component of friction between two oblique crossing fibers. A relatively simple and original statistical approach has also been developed to evaluate the confidence interval of friction coefficient. The first results show a relative stability of the transverse friction. This coefficient is also significantly inferior to the longitudinal one.