In summary, stresses ${\sigma }_x$ and ${\sigma }_y$ acting simultaneously produce strains in three directions:

$$\begin{gathered} {\epsilon }_x=\frac{1}{E}\left({\sigma }_x- \nu {\sigma }_y\right) \\ {\epsilon }_y=\frac{1}{E}\left({\sigma }_y- \nu {\sigma }_x\right) \\ {\epsilon }_z=-\frac{\nu }{E}\left({\sigma }_x+ {\sigma }_y\right) \end{gathered}$$

Strains ${\epsilon }_x$ and ${\epsilon }_y$ produce stresses in the $x$ and $y$ directions:

$$\begin{gathered} {\sigma }_x=\frac{E}{\left(1 - {\nu }^2\right)} \left({\epsilon }_x+ \nu {\epsilon }_y\right) \\ {\sigma }_y=\frac{E}{\left(1 - {\nu }^2\right)} \left({\epsilon }_y+ \nu {\epsilon }_x\right) \end{gathered}$$