In the present work, the Cosserat micro-polar continuum theory is introduced into the FEM numerical model, which is used to simulate the strain localization phenomena under static and dynamic loading conditions. The numerical studies on progressive failure phenomena, which occur in a panel, characterized by strain localization due to strain softening and its development, are numerically modelled by two types of Cosserat continuum finite elements, i.e. u8ω8 and u8ω4 elements. It is indicated that both two Cosserat continuum finite elements possess better performance in simulation of strain localization. Because of the presence of an internal length scale in Cosserat continuum model a perfect convergence is found upon mesh refinement. A finite, constant width of the localization zone is computed under static as well as under transient loading conditions.