In order to determine the history of the distribution of the stress and deformation state in the process of elasto-plastic deformation, it is necessary to perform integration over time during the entire deformation process. This can be achieved after formulating a suitable variational principle that is valid under conditions of finite deformations, and in which a constitutive law of incremental type for elasto-plastic deformation is incorporated. The finite element method is then the most suitable for determining the numerical solution of specific problems. Bearing the above in mind, in this work a potential function with a corresponding variational integral was derived for the case of isothermal and isotropic, time-independent elasto-plastic deformation.