A relatively large quantity of sample solutions have to be prepared for the radiochemical analysis of solidified products yielded by a plasma melting treatment of non-metallic radioactive wastes. In order to dissolve a sample of solidified products rapidly, a dissolution method with microwave heating devices was applied. In a conventional method involving only external heating with various mixtures of acids (HNO3, HF, HClO4 and H2SO4), a 0.1 g amount of the sample was dissolved with difficulty. However, upon applying the microwave-assisted dissolution method, a 1 g amount of the sample was completely dissolved in a shorter time. Thereby the time for dissolution procedures was shortened to less than one-tenth. The present dissolution method was successfully applied to blast furnace slag as a reference material to determine the main elements with good precision.