This study aimed to develop a numerical solver to calculate the magneto-hydrodynamic (MHD) signal produced by blood flow in the great vessels of the heart in a static magnetic field. This MHD signal is able to non-invasively characterize cardiac blood flow in order to supplement the present non-invasive techniques for the assessment of heart failure conditions. To characterize and eventually optimize MHD measurements, we developed a MHD solver based on a finite element code. This code was validated against literature, experimental and analytical data, and shows good agreement with all three reference values.