A device for measuring the mass of a flowing medium. The device includes a flat carrier to which at least one resistor layer is applied. Electrical conductor connections extending in alignment with one another are fixed on one end, with ends in elastic holder bodies and oriented with ends toward the carrier. On the other end, the ends of the electrical conductor connections rest with support segments each on one end face of the carrier and with fastening segments partially encompassing and gripping the carrier. The fastening segments are soldered or welded to a connecting layer or directly to the temperature-dependent resistor. As a result, the soldered or welded connection is held in a flexion-free and thrust-free manner on the fastening segments.