Surface stress was first defined by Josiah Willard Gibbs (1839–1903) as the amount of the reversible work per unit area needed to elastically stretch a pre-existing surface. Depending upon the convention used, the area is either the original, unstretched one which represents a constant number of atoms, or sometimes is the final area; these are atomistic versus continuum definitions. Some care is needed to ensure that the definition used is also consistent with the elastic strain energy, and misinterpretations and disagreements have occurred in the literature.
A similar term called "surface free energy", the excess free energy per unit area needed to create a new surface, is sometimes confused with "surface stress". Although surface stress and surface free energy of liquid–gas or liquid–liquid interface are the same, they are very different in solid–gas or solid–solid interface. Both terms represent an energy per unit area, equivalent to a  force per unit length, so are sometimes referred to as "surface tension", which contributes further to the confusion in the literature.