The paper presents a coupled model of linear induction pump for liquid metal. The magnetic filed in the motionless domains is computed by finite elements analysis while the filed inside the moving parts are computed by Fourier transform and spectral decomposition on Hermite basis. The paper is focused on the analysis of the force density according to the current supply and speed variations. Index Terms-eddy currents, finite element methods, linear induction pumps, force density, Hermite functions