A computational analysis is performed to investigate the suppression mechan
ism of magnetohydrodynamic (MHD) instability. Three different techniques ha
ve been considered which allow us to reduce the total growth of the instabi
lity: 1. doublecascades liner; 2. linear rotation and 3. externally generat
ed axial magnetic field. Double gas-puff with specifically structured densi
ty: massive inner shell and light outer one for a given current shape makes
it possible to suppress significantly the MHD instability evolution. Possi
ble mechanism of the instability dumping has been proposed. The load design
is being analyzed for the case of liner rotation with initial angular velo
city. Different values of the velocities have been considered. The using of
an external magnetic field allows us to suppress the instability when the
field reaches the specified shape and optimal value. The estimation of the
fraction of magnetic energy and energy of rotation in the full energy of th
e liner is done. The influence of axial field on MHD instability growth is
analyzed.