A container (1) for storing products comprises a tub (2) and a cover (3) which is equipped with a seal (20) positioned in a peripheral groove (10) formed in the inner face (8) of the cover (3). The container (1) is characterized in that the tub (2) comprises an inner (5) and outer (6) flat peripheral rim, the cover (3) comprising a vertical peripheral rim (7) designed to cover the outer peripheral rim (6) upon closure of the cover (3), and in that the inner (5) and outer (6) peripheral rims are in different planes and constitute a shouldered shape, the cover (3) comprising, between its vertical peripheral rim (7) and its inner face (8), a clearance (9) with a shape matching said shouldered shape of the tub (2), the distance between the plane of the clearance (9) and the plane of the inner face (8) of the cover (3) being less than the distance separating the planes of the peripheral rims of the tub (2).