Based on a thermomechanically consistent mechanical model, the constitutive law for a class of complex two-phase materials with locking-in inter-phase residual stress capability is proposed. The developed model contains the current plastic strain in its hereditary integral so that the main features of the above materials subjected to cyclic loading can be well described. The developed model can include both the endochronic constitutive equation and Bower' s empirical formula as special cases. The cyclic plasticity and ratcheting of OFHC copper (single-phase material) and rail steel BS1l(two-phase material)are analyzed and compared with experimental results