Abstract: A device for heating substances under the development of high pressures in a microwave field is disclosed. Those parts of the device lying in the microwave field comprise material transparent to microwaves. The device comprises a pressure-resistant cylindrically shaped outer container and a cylindrically shaped inner container disposed inside the outer container. Both the inner and outer container is provided with a cover or a cap for closure thereof. An interspace is provided between an inner jacket surface of the outer container and an outer jacket surface of the inner container, which space is connected with a space outside the device via connecting channels. The interspace preferably contains a cooling media which is transported to and from the interspace and outer space via the connecting channels.