A sensor device comprises a sensitive element (1) and a support (2) for the sensitive element, the support having a surface (3) with an access opening (4) to the sensitive element (1). A layer of adhesive material (5) covers at least parts of the surface (3). A venting medium (6) extends over the entire surface (3) of the support (2) and the access opening (4) and is attached to the support (2) by the layer of adhesive material (5).