This paper deals with the effective constitutive behavior of ductile metals reinforced by aligned spheroidal inclusions with linear-elastic properties. For simplicity, both the matrix and the inclusions are assumed to be incompressible and isotropic, so that the overall constitutive behavior of the metal-matrix composites is incompressible and transversely isotropic. Based on a recently proposed variational method for estimating the effective behavior of nonlinear composites, results are obtained for the initial yield surfaces and overall stress- strain relations in terms of the three essentially distinct loading modes for this class of composites: axisymmetric tension (relative to the symmetry axis of the inclusions), longitudinal shear (along the symmetry axis) and transverse shear (perpendicular to the symmetry axis).