In real conditions, a great majority of machine and structure elements and parts (shafts, pins, axis, etc.) are subjected to bending. That’s why the study of elastic plastic bending has a wide engineering science background and a very broad field of application. This work presents analytical research of elastic plastic pure bending of rectangular cross-section element. The simple power relation expresses stress strain curve in the region of uniform plastic deformation. Derived mathematical relations allow to calculate deviation of dimensionless stress neutral axis from symmetry axis of an element and dimensionless pure bending moment versus monotonic strain. Theoretical curves for different material constants are drawn. Theoretical curves of dimensionless pure bending moment give tolerable coincidence with experimental date. Derived relationships can be also fitted to analysis of rectangular cross-section element loaded by low cycle pure bending.