Mathematically, the stress at some point in the material is a plane stress if one of the three principal stresses (the eigenvalues of the Cauchy stress tensor) is zero.  That is, there is Cartesian coordinate system in which the stress tensor has the form  
For example, consider a rectangular block of material measuring 10, 40 and 5 cm along the , , and , that is being stretched in the  direction and compressed in the  direction, by pairs of opposite forces with magnitudes 10 N and 20 N, respectively, uniformly distributed over the corresponding faces.  The stress tensor inside the block will be
More generally, if one chooses the first two coordinate axes arbitrarily but perpendicular to the direction of zero stress, the stress tensor will have the form
and can therefore be represented by a 2 × 2 matrix,