A rigid pack of substantially parallelepiped appearance for tobacco products appears as a container (5) with an open top end (6), surmounted by a lid (7) hinged to the container (5) and rotatable between positions in which the top end (6) is open and closed. The pack (1) presents four lateral faces (17, 18, 19), and two end faces (12, 16) disposed mutually parallel and perpendicular to the lateral faces (17, 18, 19); at least one of the six faces (12, 16, 17, 18, 19) presents a raised portion (22) with an outwardly directed convex profile obtained by plastically deforming at least one panel (43, 44) of a blank (31) before the blank is folded around the tobacco products to fashion the pack (1).