Active plasma lenses are promising technologies for the focusing of high brightness electron beams due to their radially symmetric focusing and their high field gradients (up to several kT/m). However, in a number of experimental situations, the transverse non-uniformity of the current density flowing in the lens causes beam emittance growth and increases the minimum achievable spot size. To study the physics of the capillary discharge processes employed as active plasma lenses, we developed a 2-D hydrodynamic computational model. Here, we present preliminary simulation results and we compare the computed magnetic field profile with one from literature, which has been experimentally inferred. The result of the comparison is discussed.