We have studied magnetothermal instabilities, giant flux jumps, both theoretically and experimentally. Magnetostriction and magnetization hysteresis loops with flux jumps were calculated over a wide range of experimental parameters employing two critical-state models: the Kim-Anderson model and the exponential model. The influence of the magnetic history on the flux jumps' magnetostriction and magnetization were investigated for the LaSrCuO single crystal. The shape of the unstable region of the critical state in the temperature-magnetic field plane was constructed from calculations and experimental results. In the Kim-Anderson model H-T diagrams of flux instabilities agree well with experimental results on HTSC single-crystal LaSrCuO and experimental results on LTSC niobium.