The effect of an axial magnetic field on the flow produced by counter rotation of the top and bottom disks in a truncated conical enclosure filled with a liquid metal is studied The governing Navier Stokes, and potential equations are solved by using the finite volume method . It was observed that the Reynolds num ber is increased, the axisymmetric basic state loses stability and giving an asymmetric mode m=1. It is also found that the primary thresholds Re cr corresponding to the modes m=1 increase with increasing of the Hartmann number (Ha). Finally, stability diag ram (Re Ha) has been established according to the numerical results of this investigation.