A stack of interlocked detachable bags, preferably formed from a thermoplastic foil strip, and each comprising two walls, a front wall and a back wall, preferably at least one handle-shaped incision positioned on one of said walls adjacent an upper filling opening, wherein the individual bags each have an interlock piece and are attached together with the aid of at least one interlock means engaging their interlock pieces, and by means of a row of perforations forming an edge of the interlock piece the individual bags are detachable from the interlocked stack by tearing off. On one of the walls of each bag adjacent an upper filling opening edge of that bag a reinforcing piece, preferably of plastic foil, with the interlock piece is attached so that the interlock piece protrudes above the filling opening edge. Advantageously the inside of the back wall is provided with the protruding interlock and reinforcing pieces. The interlock means is put into the interlock pieces of the stacked individual bags to form the stack of interlocked detachable bags. A process for making the stack of interlocked detachable bags is also described.