Abstract: In the microwave oven of square waveguide type or coaxial tube type, the waveguide or inner conductor of the tube type is gradually declined from the inlet toward the outlet of the oven. A top slot is provided so that containers may be moved along the slot with their bottom portions being received in the oven and the contents heat sterilized. There is laid on a bottom surface of the oven a support rail for the bottoms of the containers, and this rail is gradually thickened from the inlet toward the outlet. More preferably, two or more such microwave ovens may be serially connected and the containers may be moved therethrough to heat sterilize medical fluids within each container in a stepwise manner.