The study of packed beds of granular spheres and their applications are of great interest to industries, and one of the most important subjects that has been studied is cylindrical beds. In 1895, H. A. Janssen discovered that in a vertical cylinder the pressure measured at the bottom does not depend upon the height of the filling in contrast to Newtonian fluids that possess linear hydrostatic pressure equilibrium. One of assumptions of his theory stated that the horizontal pressure is proportional to the vertical. In this thesis, this physical hypothesis is investigated using Discrete Element Simulations of inelastic with a cylindrical vessel and an axial pressure load. In addition, we studied the radial solid fraction to better understand the pattern of radial pressure evolution. The force model that corresponds to linear spring-dashpot model and energy dissipation is simulated by frictional forces: inter-particle and particle-wall. In this model, the frictional forces at the wall are activated by moving the piston floor downwards with small velocity. The diameter of the cylinder is set to 13.33 diameters of particle and the fill heights are in the range from 0.262 to 10.172. Results obtained in the simulations show the limits of Janssen's theory applicability within granular physical phenomenon, and also provide a strong foundation for further theoretical analysis.