Summary From the continuum mechanics points ofview, most of commercial fibre-reinforced composites (FRCs) can be considered to be anisotropic materials with one of the five material symmetries: transverseisotropy, orthotropy, tetratropy, hexatropy and octotropy, as illustrated in the preceding paper (Part I) [1]. No properly general formulation of constitutive equations for tetratropic, hexatropic and octoctropictypes of FRC has been found in the literature. In this paper, the restriction to the admissible deformationof a FRC imposed by the failure strains of the fibres is investigated. The complete and irreducibletwo-dimensional tensor function representations regarding tetratropy, hexatropy and octotropy derivedin Part I are applied to formulate constitutive equations for FRCs in plane problems of elasticity, yieldingand failure in the present work, and of heat conduction, continuum damage and asymmetric elasticityin a continued work (Part III, forthcoming).