The present article consists in the modelling an design of a Paul ion trap using the Method of Moments for numerical integration. Firstly, we have developed some preliminary work with simple geometries in two and three dimensions. Then we have designed the geometry of the trap, consisting in two hiperboloid plates which have been discretized, triangulated, and solved by the Method of Moments. The potential in the plates has been set to vary harmonically, since sinusoidal signals have proved to be more e ective than triangular and square signals. We have then simulated the con nement of one, two and multiple ions, and we have studied how the chosen frequency and potential a ect the e ectiveness of the trap 2020/2021