Based on the form of the Tsai-Hill criterion, a new failure criterion for anisotropic material subjected to combined stress is developed and demonstrated. It is capable of accurately calculating the strength of anisotropic materials. The generality and accuracy of the present failure criterion are illustrated by examination through the use of Kraft paperboards under various loading conditions. Compared to the Tsai-Hill theory, which is much too conservative at high levels of shear stress, the present criterion has a good agreement with the experimental data. It also has the ability to calculate the strength more simply, compared to the Tan-Cheng theory.