An approximate nonlinear theory is developed to describe waveguide‐type propagation in unidirectional fibrous composites. The model, which is an extension of a previously developed laminate formulation, explicitly considers the effects of thermodynamics, finite deformations, and nonlinear (elastic‐plastic) constitutive behavior. The theory contains microstructure and yields information on stress, deformation, and internal energy within individual components. The resulting equations assume the form of a one‐dimensional binary mixture theory. Transient wave propagation solutions are obtained numerically, and are compared with essentially exact data from a well‐known two‐dimensional finite difference code in an effort to extract information concerning accuracy and computational economy of the mixture model.