The advantages of the dielectric disc resonators working in whispering gallery modes for applications at millimeter and submillimeter wavelengths are discussed. The characteristics of such resonators are reviewed in the light of spectroscopic applications. The theoretical description of the different wave equation solutions in these structures is shortly outlined. The experimental arrangement for measurements at 240 GHz is accurately analyzed; a special care is devoted to the radiation transmission and coupling lines and to the measurement of the spatial distribution of the energy for the different modes. Experimental results are compared with data obtained with the approximate analytical mode description.