This article proposes two constitutive models to describe the nonlinear, elastic-plastic behavior of unidirectional fiber-reinforced composites at the meso-level. Key ingredients are the formulation of two anisotropic yield functions with the aid of representation theorems (invariant formulation), and the set-up of governing equations for plastic variables with respect to associative and non-associative flow response. The governing equations are solved using an elastic predictor-plastic corrector algorithm which imposes the constraint posed by the yield condition. Both the models are evaluated qualitatively and quantitatively by comparison to micromechanics simulations as well as to experimental data.