This article investigates the effect of using isotropic and anisotropic plastic response functions in the analysis of the elastic-plastic response of unidirectional fiber composites on the meso-scale. Three model problems that use a Drucker-Prager-type pressure-dependent yield function are considered to simulate the nonlinearities exhibited by a composite material. A further core ingredient is the analysis of a canonical and nonconventional constitutive structure, with respect to associated and nonassociated flow response, where the use of latter is motivated by the physical inconsistencies induced by the former under shear dominated loads. These models are evaluated quantitatively by comparison to experimental data.