A geometrically non-linear formulation for composites and the resulting explicit dynamic "nite element algorithm are presented. The proposed formulation assumes that small elastic and large plastic strains, being the anisotropy considered using tensors which map the model variables at each time step into an equivalent isotropic space, where the integration of the rate constitutive equations is performed. The evolution of the internal variables is calculated in the auxiliary spaces, taking into account the material non-linear behaviour, and the results mapped back to the real stress space. The updating of the mapping tensors for each new spatial con"guration allows the treatment of general anisotropic materials under large strain and can be extended to treat multiphase composite materials using the mixing theory. The behaviour of the composite is dictated by the mechanical response of each substance, and the resultant model allows a fully non-linear analysis combining di!erent material models, such as damage in one compounding substance, elastoplastic behaviour in the other, while a third substance behaves elastically.