The maximum stress criterion states that failure occurs when the maximum (normal) principal stress reaches either the uniaxial tension strength s_t, or the uniaxial compression strength s_c,

where s₁ and s₂ are the principal stresses for 2D stress.

Graphically, the maximum stress criterion requires that the two principal stresses lie within the green zone depicted below,

Mohr's theory suggests that failure occurs when Mohr's Circle at a point in the body exceeds the envelope created by the two Mohr's circles for uniaxial tensile strength and uniaxial compression strength. This envelope is shown in the figure below,

The left circle is for uniaxial compression at the limiting compression stress s_c of the material. Likewise, the right circle is for uniaxial tension at the limiting tension stress s_t.

The middle Mohr's Circle on the figure (dash-dot-dash line) represents the maximum allowable stress for an intermediate stress state.

All intermediate stress states fall into one of the four categories in the following table. Each case defines the maximum allowable values for the two principal stresses to avoid failure.

Case	Principal Stresses		Criterion requirements
1	Both in tension	s1 > 0, s2 > 0	s1 < st, s2 < st
2	Both in compression	s1 < 0, s2 < 0	s1 > -sc, s2 > -sc
3	s1 in tension, s2 in compression	s1 > 0, s2 < 0
4	s1 in compression, s2 in tension	s1 < 0, s2 > 0

Also shown on the figure is the maximum stress criterion (dashed line). This theory is less conservative than Mohr's theory since it lies outside Mohr's boundary.