The objective of this study is to model and simulate the equations of motion for a conceptual prototype of micro-robot powered by four propellers made of rigid helices and of a cargo head shaped as an ellipsoid. A finite element code has been developed, intended to simulate the Stokes flow in order to derive the hydrodynamic resistance coefficients by comparing them with those present in the literature. To achieve this as reliably as possible, benchmark cases are studied using a sphere and an ellipsoid whose coefficients can be obtained through analytical formulae. The solutions of these two cases allow to compare the streamlines, the velocity and pressure fields used to validate the code.