The self-propelling motion of the flexible ferromagnetic swimmer is described. Necessary symmetry breaking is achieved by the buckling instability at field inversion. The characteristics of self-propulsion are in good agreement with the numerical calculations of the Floquet multipliers for the ferromagnetic filament under the action of ac magnetic field. In the low frequency range the power stroke of self-propelling motion is similar to that used by the unicellular green algae chlamydomonas and in the high frequency region the self-propulsion is due to the undulation waves propagating from the free ends perpendicularly to ac magnetic field.