The effect of the plasma impedance in the problem of the inverse pinch is investigated. The initial value problem is formulated with respect to the electric current and the magnetic cavity radius in the frame work of the reasonable approximations. Especially, there needs no assumption about the time variation of the electric current. The solution is obtained numerically by the usual method of quadrature, while the initial period of time is examined analytically. The asymptotic approach to the final equilibrium state is investigated by the PLK method of approximation. Representative cases are investigated in detail and it is shown that the duration time of the transient variation is very long in comparison with the operation time of the ordinary intermittent type MHD devices.