The concept of stress originated from the study of strength and failure of solids. The stress field is the distribution of internal "tractions" that balance a given set of external tractions and body forces.

First, we look at the external traction T that represents the force per unit area acting at a given location on the body's surface. Traction T is a bound vector, which means T cannot slide along its line of action or translate to another location and keep the same meaning.

In other words, a traction vector cannot be fully described unless both the force and the surface where the force acts on has been specified. Given both DF and Ds, the traction T can be defined as

The internal traction within a solid, or stress, can be defined in a similar manner. Suppose an arbitrary slice is made across the solid shown in the above figure, leading to the free body diagram shown at right. Surface tractions would appear on the exposed surface, similar in form to the external tractions applied to the body's exterior surface. The stress at point P can be defined using the same equation as was used for T.

Stress therefore can be interpreted as internal tractions that act on a defined internal datum plane. One cannot measure the stress without first specifying the datum plane