Discontinuous fiber reinforced plastics have superior productivity and formability in comparison with continuous fiber reinforced plastics. However, their strengths are remarkably low. Thus there is an urgent need to establish a fundamental model in order to improve the strength of discontinuous fiber reinforced plastics. In the present work, we utilized numerical simulations that consider the microscopic damage in the composite and incorporate an individual constitutive law of thermosetting resin or thermoplastic resin. The fundamental mechanism that affected the strength and failure of the composite was investigated when the fiber length and/or matrix properties were varied from continuous glass fiber reinforced plastics to discontinuous glass fiber reinforced plastics. Our results clarified two factors that cause the strength degradation of discontinuous fiber reinforced plastics. One is the low yield stress of thermoplastic resin, which is frequently used for the matrix of discontinuous fiber reinforced plastics. As the other factor, the final failure mode is changed from fiber breaking mode to matrix cracking mode in the case of the low fiber volume fraction of discontinuous glass fiber reinforced plastics. Moreover, we investigated the relationship between fiber length and strength of carbon fiber reinforced polypropylene and the effect of thermoplastic matrix properties depending on the loading rate as well.