The information in the basic references about the relation between elastic constants and particularly Young's modulus (E) behavior and plastic deformation indicates that this parameter is constant or almost constant. At the beginning of the XX century several authors indicated that E of some metals decreased when cold deformation increased and detected reductions up to 15% in steels, aluminum, copper, brass... In the last years this behavior is taking into account during the finite-element analysis of sheet metal stamping or other plastic deformation processes. This work includes an extensive review of papers of our research team and of other authors related with the behavior of Young's modulus during plastic deformation of some metallic alloys. This parameter can diminish up to 10% by plastic deformation (tension test) in iron, aluminum, and stainless steel (UNS S 30403) but remains practically unaltered in aluminum alloys deformed before or after aging. Results of Young's modulus in nanostructured copper and copper alloys determined by ultrasonic technique are also presented. Additional results of Young's modulus of UNS G10180 and UNS G10430 steels measured during loading and unloading steps in tension test are also included. High differences in the E values were detected between both steps.