A machine for making filter bags for infusion products formed from lengths of filter material, characterized in that it comprises at least: - a station for feeding a first continuous strip of thermoformable filter material movable along a working path; - a station for heating the first continuous strip, located along the working path and including means for heating the first continuous strip of thermoformable filter material at a predetermined temperature; - a drum for forming a first portion of the filter bag disposed downstream of the station for heating along the working path; said drum having two mutually concentric circular parts (6,7) continuously rotating in phase about a single axis of rotation so as to configure an annular zone where the first continuous strip is interposed; a first circular part of the drum being provided with a series of radial dies, and a second part having a corresponding series of forming punches for forming the first strip of filter material and adapted to plastically deform a portion of the first strip of filter material inside a corresponding die at least for a predetermined arcuate stretch of a circular path followed by the drum, so as to form an open three-dimensional chamber of filter material; - a station for dosing a dose of infusion product and configured for placing, the dose, in phase with the drum, inside the open three-dimensional chamber of filter material; - a station for feeding a second continuous strip of filter material and configured for placing the second continuous strip above the first continuous strip with the three-dimensional chambers with the dose of infusion product, so as to define a flat base that closes the filter bags; - a station for joining / closing the second continuous strip of filter material onto the first continuous strip of filter material and located along the working path, downstream of the station for feeding the second continuous strip of filter material; - a cutting station for making a sequence of single, flat-based filter bags by cutting the first and the second continuous strip (3, 14) of filter material; the cutting station being located downstream of the joining / closing station along said working path. - a station for feeding a first continuous strip of thermoformable filter material movable along a working path; - a station for heating the first continuous strip, located along the working path and including means for heating the first continuous strip of thermoformable filter material at a predetermined temperature; - a drum for forming a first portion of the filter bag disposed downstream of the station for heating along the working path; said drum having two mutually concentric circular parts (6,7) continuously rotating in phase about a single axis of rotation so as to configure an annular zone where the first continuous strip is interposed; a first circular part of the drum being provided with a series of radial dies, and a second part having a corresponding series of forming punches for forming the first strip of filter material and adapted to plastically deform a portion of the first strip of filter material inside a corresponding die at least for a predetermined arcuate stretch of a circular path followed by the drum, so as to form an open three-dimensional chamber of filter material; - a station for dosing a dose of infusion product and configured for placing, the dose, in phase with the drum, inside the open three-dimensional chamber of filter material; - a station for feeding a second continuous strip of filter material and configured for placing the second continuous strip above the first continuous strip with the three-dimensional chambers with the dose of infusion product, so as to define a flat base that closes the filter bags; - a station for joining / closing the second continuous strip of filter material onto the first continuous strip of filter material and located along the working path, downstream of the station for feeding the second continuous strip of filter material; - a cutting station for making a sequence of single, flat-based filter bags by cutting the first and the second continuous strip (3, 14) of filter material; the cutting station being located downstream of the joining / closing station along said working path.