A torque fluctuation absorbing apparatus is capable of securely sealing a space housing an elastic member even on application of a centrifugal force or at the time of cooling. The torque fluctuation absorbing apparatus includes a center plate, a side plate(s) (side plate assembly) coaxial with the center plate and slidably relative to the center plate, and an elastic member housed within a space delimited by the side plate assembly to absorb torque fluctuations between the side plate assembly and the center plate. The apparatus also includes a cover member secured to the center plate and slidably pressure contacted with the side plate assembly to cover from outside a space housing the elastic member, and a suppressing section capable of suppressing the cover member from deforming under a pressure acting on the cover member when atmospheric pressure within the space housing the elastic member(s) becomes lower than outside atmospheric pressure.