The compression test provides a useful information about the material flow under large plastic deformations, when compared to the standard tensile test. On the other hand, it is heavily dependent on the lubrication conditions. The paper deals with two different specimen geometries resulting in two different friction conditions. The first geometry corresponds to the classical smooth cylinder. The second one was designed according to the idea of Rastegaev. It is a smooth cylinder with grooves on both faces (bases), which allow the lubricant to accumulate and prevent it from escaping the region, where the punches are in the contact with specimen. Then, both cases were computationally simulated and compared with experiments.