In the present work, a simulation system is proposed that can be used as an educational tool by physicians in training basic skills of minimally invasive vascular interventions. In order to accomplish this objective, initially the physical model of the wire proposed by Konings has been improved. As a result, a simpler and more stable method was obtained to calculate the equilibrium configuration of the wire. In addition, a geometrical method is developed to perform relaxations. It is particularly useful when the wire is hindered in the physical method because of the boundary conditions. Then a recipe is given to merge the physical and the geometrical methods, resulting in efficient relaxations. Moreover, tests have shown that the shape of the virtual wire agrees with the experiment. The proposed algorithm allows real-time executions, and furthermore, the hardware to assemble the simulator has a low cost.