A rigid container for tobacco items, defined by a tubular lateral wall (11) and by at least one end wall (6), and wherein one of the two walls (6, 11) has at least one inwardly concave portion (13; 82; 91; 96; 102; 113), and the other wall has at least one flat portion (8; 114), which mates with the concave portion (13; 82; 91; 96; 102; 113) along a convex outer edge portion (10, 115) of its own, and is formed from a panel (6′; 6′, 6″; 121a, 122a) having a first portion (6′a; 6′a, 6″a; 128) corresponding to the flat portion (8; 114), and a peripheral second portion defined by at least one curved strip (20; 20′, 20″; 127) bounded internally by a curved crease line (19; 19′, 19″; 126) extending along the convex outer edge portion (10; 115); the strip (20, 20′, 20″; 127) being folded squarely, by drawing, to define a convex border (23; 129) extending along the convex outer edge portion (10; 115), and being made integral with an inner surface of the concave portion (13; 82; 91; 96; 102; 113).