A pressure pulsation absorbing device adapted to be connected between a pair of piping flanges includes a cup-shaped silencer box having a central inner bore for fluid flow therethrough, and a plurality of water stop bosses integrally formed with the silencer box around the inner bore and through which piping bolts are to be inserted. An elastic cylindrical body is provided in the silencer box around the water stop bosses to thereby divide the inside space of the silencer box into a radially inward fluid flow section and a radially outward dry section. A plurality of threaded bosses are integrally formed with the silencer box in the dry section for receiving bolts for fixing a side plate covering a side opening in the dry section. A slight clearance is provided respectively between outer surfaces of the water stop bosses and an inner circumference of the cylindrical body, and between outer surfaces of the threaded bosses and an outer periphery of the cylindrical body. The pressure pulsation is absorbed by expansion and contraction of the elastic cylindrical body. However, such expansion and contraction is limited within the range of the slight clearances and, therefore, breakage of the elastic cylindrical body is prevented.