A sound suppression system for reducing or eliminating sound produced by the operation of a breast vacuum pump includes a sound suppressing muffler assembly having an air entry port adapted to communicate with an air outlet port of a vacuum pump or other air flow generating device. The sound suppressing muffler assembly also includes a muffler housing defining an internal space communicating with the air entry port, and an opening in the housing leading to atmosphere. The muffler housing has a tortuous air path in the muffler housing. In one embodiment, sound absorbing porous foam structure is disposed in the tortuous air path. The at least one sound absorbing porous structure absorbs sound energy from the air as the air moves through the at least one air path toward the opening in the muffler housing. In further embodiments, a tortuous air path is provided between an air entry port and an opening to atmosphere in the muffler assembly.