A method of drying transport and/or storage containers for radioactive waste has the first step draining or pumping residual water out of the container holding the nuclear waste. Then gas is evacuated from the interior of the drained or pumped out container interior. Thereafter an inert gas is fed into the drained or pumped out container interior while continuing to evacuate gas from the container interior. During the evacuation and/or infeeding of inert gas a rate of evacuation and/or a rate of infeed of the inert gas is controlled such such that an inert-gas content in the interior of the container is between 50 and 95 vol %.