Sound relies upon the movement of particles of a medium for transmission, which is why sound does not travel in space. So if the medium is inelastic, sound cannot move the particles and the particles cannot push further particles, so the sound is not transmitted. Imagine a line of people standing shoulder to shoulder. If you push one person, that one pushes the next one who pushes the next one, etc. If one person is replaced by an immovable concrete pillar, that will not allow the movement to proceed. Same thing with sound.