The invention relates to a device for heat sealing two layers of foil material. To that end, the device comprises two blocks arranged opposite each other and conveying means for guiding the foil material between these blocks. Between the blocks, at least one heating element is provided, for heating the foil locally, and at least one circulating belt (20), which, in use, is guided along the blocks. The circulating belt (20) is built up from at least one layer of resilient material, so that a force applied by the blocks to the foil material is uniformly distributed over the sealing seam to be formed. The invention further relates to a circulating belt for use in a device according to the invention.