The article describes the basic concepts associated with a model for describing real processes of material deformation in the solid state, known as Madelung deformation. This model was developed by scientist Aubrey Williams Madelung based on a series of experimental data on the mechanical properties of materials. The model considers deformations at various stresses and temperatures, as well as their effect on the mechanical properties of materials, such as elastic modulus, strength and ductility. The article also describes an extended version of this model, the so-called Hill-Madelung deformation, which takes into account fatigue effects and non-equilibrium materials during deformation processes.