The invention provides a pressure sensor with a housing for a pressure sensing arrangement, e.g. a semi-conductor arrangement. The housing consists of a bottom part and an intermediate member with a through hole forming a sidewall of a cavity for the pressure sensing arrangement. A membrane is attached to the intermediate member to cover an opening of the cavity, and to allow pressure from outside to propagate into a pressure transmitting medium contained inside the housing and thus to the pressure sensing arrangement therein. The invention also provides a method of making a pressure sensor with a housing of the above-described kind.