A numerical resolution of the laminar swirling flow between two fixed cones having the same apex angle is presented in the case where the fluid is tangentially introduced at the system base. The resolution of the momentum and continuity equations is done by using an implicit finite different scheme. Two conical configurations are considered. In the first one, named CG1, the apex of the cones generatrix is located at the top with respect to the fluid entrance, in the second one, named CG2, the apex is down. The calculations, which concern the three components of the velocity flow-field and the pressure, allowed us to compare the swirl properties in the two studied situations with respect to a similar system made of two coaxial cylinders. The swirl intensity, calculated from the velocity field revealed that in the CG1 case the swirling motion is stronger and the swirl decay is delayed in comparison with the CG2 and the cylindrical cases.