We present the results of numerical simulations of the formation and development of magnetized jets. We simulate a plasma flow, for which we chose a numerical method, boundary and initial conditions. We investigate the picture of the flow for different magnetic field configurations. We compared these results with the experiment on a NEODIM laser installation. In the absence of a magnetic field, a substantial expansion of the jet occurs. In the presence of a strong poloidal magnetic field, the jet expands only slightly, which confirms the possibility of a magnetic collimation mechanism for astrophysical jets. Under certain values of the magnetic field a ring structure may form. The opening angle of these simulated structures approximates the results of the laboratory experiment.