Next, the generalized Hooke's Law stress-strain relationships will be used to determine the normal stresses corresponding to the principal strains. Although the Hooke's Law equations are written in terms of x and y, they are applicable for any pair of orthogonal axes. In this instance, the axes being considered are the p1 and p2 directions, corresponding to the principal strain directions.

${\mathrm{\sigma }}_{\mathrm{x}}=\frac{\mathrm{E}}{(1-{\mathrm{\nu }}^2)}({\mathrm{\epsilon }}_{\mathrm{x}}+{\mathrm{\nu \epsilon }}_{\mathrm{y}})$

${\sigma }_y=\frac{E}{(1-{\nu }^2)}({\epsilon }_y+\nu {\epsilon }_x)$