Abstract: A semiconductor pressure sensor (10) includes a substrate (12) as semiconductor material which comprises an active surface (14) for receiving integrated components (26, 28) and a rear side (16) in which to form a diaphragm (20) adjoining the active surface (14) and exposed to the pressure to be measured a recess surrounded by thick edge regions (22, 24) is formed. On the active surface (14) integrated components are provided which under the influence of mechanical deformations of the diaphragm (20) vary one of their electrical parameters. The substrate (12) is connected to the support element (34) in the region of the active surface (14) surrounding the diaphragm (20) by using an elastomer seal (40). The diaphragm (20) is in communication from the rear side of the substrate (12) with a supply conduit (44) for the pressure to be measured.