Materials failure under some sort of loading is a well-known natural phenomenon, and the reliable prediction of materials failure is the most important key issue for many different kinds of engineering structures based on their safety considerations. In this research, instead of establishing empirical models, the material failure process was modeled as a nonequilibrium process based on the microstructural mechanism. Then, the evolution equations were established and the stability analysis was carried out to obtain the critical conditions for the materials failure. It was found that the material strength was a global property in nature, and the commonly used local criteria based on the most dangerous point failure were not the rational assumption. Based on the idea,some examples were considered, such as the size effect of the material strength, the strength of the polycrystalline metals, the stress-strain relationship of the ultrafine crystalline metal with nanoscale growth twins, the strength of lithium niobite crystal specimens with notches. All of the theoretical predictions gave reasonable results compared with the experimental data.