In a positive displacement machine for compressible media, having a spiral-shaped feed chamber (11) arranged in a housing (7b) between cylinder walls (14, 15), a spiral-shaped displacement body is composed of a disc (2) with spiral-shaped strips (3). The strips (3) are held eccentrically with respect to the housing, in such a way that, during operation, each point of the strip performs a movement which is limited by the peripheral walls of the feed chamber. The contour (20) of the disc is formed, in the overlapped region of the spiral at the point provided for the mutual sealing of the traversed chambers (11, 16), in the shape of the movement path. The housing edge (19) is formed, as a transition between the raised first part (17) and lowered second part (18) of the outer cylinder wall (14) of the housing, as a bulbous thickened portion. The radial extent “D” of the thickened portion is at least as great as the degree of eccentricity (“e”). In periods of machine operation, in which a higher pressure prevails in the outer, sickle-shaped working space (11) than in the suction chamber (16), the circular-arc-shaped projection (19) together with the contour of the disc forms a sealing line (21) which extends over the height of the projection.