Failure analyses of laminated fibrous composite structures were conducted using the failure criteria based on a multiscale approach. The failure criteria used the stresses and strains in the fiber and matrix materials, respectively, rather than those smeared values at the lamina level. The failure modes and their respective failure criteria consist of fiber failure, matrix failure and their interface failure explicitly. In order to determine the stresses and strains at the constituent material level (i.e. fiber and matrix materials), analytical expressions were derived using a unit-cell model. This model was used for the multiscale approach for both upscaling and downscaling processes. The failure criteria are applicable to both quasi-static loading as well as dynamic loading with strain rate effects.