The matrix phase of fiber-reinforced polymer-matrix composites typically exhibits nonlinear viscoelastic/viscoplastic behavior with damage evolution. For the structural safety evaluation, these polymer characteristics should be appropriately modeled to predict crack initiation on the fiber-diameter scale accurately. In this study, the matrix modeling effect on multiscale prediction of nonlinear response and crack initiation was investigated using a multiscale approach that consists of two finite-element analysis on different length scale. On the macroscopic scale, laminate-scale finite-element analysis assuming to be a homogeneous orthotropic lamina was conducted to obtain strain histories at failure-expected points. On the microscopic scale, periodic unit-cell (PUC) analysis considering heterogeneous material structure was performed to predict crack initiation in the matrix phase of composite laminates, based on strain histories obtained from a macroscopic laminate analysis. Two constitutive models and four sets of failure criteria were applied to the matrix phase of the unit cell for PUC analysis, and compared with each other to evaluate important factors in multiscale prediction of polymer-matrix composites.