A sound suppressor for a firearm comprises a cylindrical housing having a proximal end with means for attachment to a firearm and to the cylindrical housing, and a distal end with means for attachment to the housing, and a plurality of baffle elements positioned within the housing between the proximal and distal ends of the suppressor. A plurality of spacer elements is positioned between the proximal and distal ends of the suppressor and between the baffle elements. The baffle element comprises a symmetrical conical baffle with a hemispherical shaped apex, with said apex being provided with a concentric hole. The symmetrical conical baffle is also provided with a plurality of steps or annular shoulders on the exterior of the conical baffle, and these annular shoulders increase in diameter with respect to their position on the exterior of the baffle and with respect to the distance from the hemispherical shaped apex of the baffle. In an alternate embodiment, the symmetrical conical baffles are provided with a flat flange that extends outwardly from the major diameter of the conical baffle to the internal diameter of the cylindrical housing. Reduced diameter spacer elements are positioned between the baffles, and the flat flange provides support and permits axial positioning of the reduced diameter spacer elements between the baffles. The reduced diameter spacer elements are positioned so that they are positioned against one of the external annular shoulders of a baffle and the flat flange of a prior baffle, and dividing the expansion chamber between baffle elements into two concentric expansion chambers. The reduced diameter spacer elements are provided with at least one gas port to allow flow of gases from the inner expansion chamber to the outer expansion chamber.