Von Mises criterion is based on the observation that a hydrostatic pressure cannot cause plastic yielding of the material. The conclusion that only the energy of distortion influences the transition from an elastic to a plastic state comes naturally. This criterion can be formulated as follows: the material passes from an elastic to a plastic state if the elastic energy of distortion reaches a critical value that is independent of the type of the stress state. The criterion may be written in the form:

(σ₁ − σ₂)² + (σ₂ − σ₃)² + (σ₃ − σ₁)² = 2σ₀²    (1)

and for plane stress (σ₃ = 0):

σ₁² + σ₂² − σ₁σ₂ = σ₀²                        (2)

This equation represents an ellipse in the plane of the principal stresses σ₁ and σ₂ circumscribing the polygon given by the Tresca criterion.