**NTRODUCTION:**

It predicts the failure of a specimen subjected to any combination of loads when the strain energy per unit volume of any portion of the stressed member reaches the failure value of strain energy per unit volume as determined from an axial or compression test of the same material.

- The total strain energy per unit volume is given by the sum of the energy component due to three principal stresses and strains.

- For a 3 - dimensional state of stress system the total strain energy Ut per unit volume in equal to the total work done by the system and given by the equation

According to this theory the materials fails when this energy equals to the limiting Energy

This is an equation of ellipse with axes at 45^{0}