Under undrained monotonic static loading, saturated loose granular materials may undergo static liquefaction. Tailings, a kind of granular material, pose particularly serious hazards after static liquefaction. To understand the effects of the initial state and fines content on the static liquefaction of tailings, consolidated undrained triaxial compression tests and one-dimensional compression tests were carried out on tailings with different initial states and fines content. The critical state strength, undrained shear strength, instability line, brittleness index, and compressibility of tailings were investigated, and the tests results were analyzed and discussed using the critical state framework. The results show that tailings with different initial states have the same critical state line, and changes in fines content will cause the position of the critical state line to shift. An increase in the initial void ratio and initial confining pressure will increase the degree of static liquefaction, while the influence of fines content has a threshold value (30%), at which the degree of static liquefaction is the highest. Our analysis shows that compressibility has limitations for evaluating static liquefaction, while the state parameter is an effective indicator for evaluating the static liquefaction of tailings with different initial states and fines contents. The results provide valuable theoretical and practical insights regarding the static liquefaction of tailings and are of great significance for evaluating the stability and preventing the static instability of tailing dams.