A method of ascertaining the state inside a melting furnace of a radioactive waste, which method comprises: blowing a gas into a molten matter in the melting furnace by using at least two slender tubes disposed at an upper and lower points with a gap .DELTA.h between said points; detecting a back pressure difference .DELTA.P at the slender tubes to determine the density .rho. of the molten matter; and determining the level h of the molten matter in the furnace using the density .rho.. It is also possible to detect the formation of a bridge inside the furnace due to a non-molten solid matter of the waste charged into the furnace.