The Tsai–Wu Quadratic Failure Criterion is a modified tensor polynomial criterion, that is widely used and the most readily accepted failure criterion for orthotropic materials. While it is an excellent criterion for the majority of composite structures, there is limited experimental validation of this criterion when predicting the failure envelope for “combined shear” failures or, better stated, failures that involve both 2-D (in-plane) and 3-D (out-of-plane) shear stresses in an orthotropic material or laminate. Since several common types of material failure involve complex stress states, the ability to incorporate the effect of 3-D shear stress into failure prediction is attractive. The 3-D Tsai–Wu quadratic failure criterion that incorporates multiple shear stresses is presented in this text and tests were conducted on several laminate specimens in an effort to validate this criterion. Failure load predictions were made to validate the modified 3-D criterion and compare the results with the 2-D Tsai–Wu criterion for specialized cases where multiple shear stresses were present at failure. This testing clearly shows strong agreement between the 3-D criterion’s predictions and experiments for these cases, implying that the standard 2-D Tsai–Wu quadratic failure criterion can be safely extended, through the addition of terms, to 3-D cases.