A rigid suitcase comprising: a first shell and a second shell which are hinged to each other and have outer surfaces (2a, 3a) and inner surfaces respectively, wherein said inner surfaces face each other to define a first storage volume, the outer surface of said first shell comprising a recess projecting into said first storage volume and delimited by a bottom wall and side walls of the outer surface of the first shell; an auxiliary container defining a second storage volume that is physically separate from said first storage volume, said auxiliary container being adapted to be moved between an inserted state, in which it is at least partially housed in said recess and a removed state, in which it is completely extracted from said recess; guide members operable between said recess and said auxiliary container and designed to guide said auxiliary container as it moves from the inserted state to the removed state and vice versa; removable attachment members operable between said first shell and said auxiliary container and adapted to be actuated between an attached state, in which the auxiliary container cannot be removed from said guide members and a released condition in which the auxiliary container may be removed from said guide members; characterized in that said bottom wall of the outer surface of said first shell in which said recess is formed or a rear wall of said auxiliary container facing said recess being concave, with a concavity facing toward the exterior of the first or second storage volumes respectively, such that the central portion of said bottom wall is farther from said rear wall than the peripheral portions of said bottom wall or such that the central portion of said rear wall is farther from said bottom wall than the peripheral portions of said rear wall respectively. a first shell and a second shell which are hinged to each other and have outer surfaces (2a, 3a) and inner surfaces respectively, wherein said inner surfaces face each other to define a first storage volume, the outer surface of said first shell comprising a recess projecting into said first storage volume and delimited by a bottom wall and side walls of the outer surface of the first shell; an auxiliary container defining a second storage volume that is physically separate from said first storage volume, said auxiliary container being adapted to be moved between an inserted state, in which it is at least partially housed in said recess and a removed state, in which it is completely extracted from said recess; guide members operable between said recess and said auxiliary container and designed to guide said auxiliary container as it moves from the inserted state to the removed state and vice versa; removable attachment members operable between said first shell and said auxiliary container and adapted to be actuated between an attached state, in which the auxiliary container cannot be removed from said guide members and a released condition in which the auxiliary container may be removed from said guide members; characterized in that said bottom wall of the outer surface of said first shell in which said recess is formed or a rear wall of said auxiliary container facing said recess being concave, with a concavity facing toward the exterior of the first or second storage volumes respectively, such that the central portion of said bottom wall is farther from said rear wall than the peripheral portions of said bottom wall or such that the central portion of said rear wall is farther from said bottom wall than the peripheral portions of said rear wall respectively.