The total potential energy, , is the sum of the elastic strain energy, , stored in the deformed body and the potential energy, , associated to the applied forces:
This energy is at a stationary position when an infinitesimal variation from such position involves no change in energy:
The principle of minimum total potential energy may be derived as a special case of the virtual work principle for elastic systems subject to conservative forces.
The equality between external and internal virtual work (due to virtual displacements) is:
where
*  = vector of displacements
*  = vector of distributed forces acting on the part  of the surface
*  = vector of body forces
In the special case of elastic bodies, the right-hand-side of () can be taken to be the change, , of elastic strain energy  due to infinitesimal variations of real displacements.
In addition, when the external forces are conservative forces, the left-hand-side of () can be seen as the change in the potential energy function  of the forces. The function  is defined as:
where the minus sign implies a loss of potential energy as the force is displaced in its direction. With these two subsidiary conditions,  becomes:
This leads to () as desired. The variational form of () is often used as the basis for developing the finite element method in structural mechanics.