Abstract: In the first part of paper, we discuss the application of the Saint-Venant's principle of the elasticity to fracture mechanics, pointing out that misusing of the principle may cause extremely large error by using sone examples. In the second part, we discuss methods for determining the shape and size of Tresca and Mises yielding surfaces and make an extension to the description of Mohr-Coulomb and Drucker-Prager yielding surfaces. We present a three-dimensional image showing the shape and size of Tresca and Mises yielding surfaces in the principal stress space to correct the errors in existing textbooks and monographs on elasto-plasticity.