Thermoforming mould device for manufacturing a thin-walled part from a sheet of thermoplastic material, the said mould device comprising two mould parts (3 and 3') with work areas (4, 4') in substantially complementary forms and of which at least one of the parts is movable so as to define a state of opening and a state of closure of the mould, a first of the two mould parts (3, 3') containing suction means in order to attach the sheet to its work area, the suction means comprising, on one hand, a main suction means suitable for generating negative pressure or suction on a majority section of the work area of the said first mould part and, on the other hand, at least one secondary suction means (5") suitable for generating negative pressure or suction at the level of at least one specific limited section of the said work area, this at least partially in an independent manner with regard to the main suction means, the or each secondary suction means (5") able to be controlled, at least to be stopped for the purpose of suspending the suction, independently of the main suction means, mould device characterised in that the second mould part comprises at least one hollow moulded part, the said part being arranged in a way to be located, when the mould is closed, directly facing the or each specific limited section respectively of the work area of the first mould part, and in that the or each hollow moulded part is movable in translation, preferably according to a direction substantially perpendicular to the work area of the second mould part or on a plane which is locally tangential to the said work area, the said part being advantageously mounted in an interchangeable manner on the said second mould part. the said mould device comprising two mould parts (3 and 3') with work areas (4, 4') in substantially complementary forms and of which at least one of the parts is movable so as to define a state of opening and a state of closure of the mould, a first of the two mould parts (3, 3') containing suction means in order to attach the sheet to its work area, the suction means comprising, on one hand, a main suction means suitable for generating negative pressure or suction on a majority section of the work area of the said first mould part and, on the other hand, at least one secondary suction means (5") suitable for generating negative pressure or suction at the level of at least one specific limited section of the said work area, this at least partially in an independent manner with regard to the main suction means, the or each secondary suction means (5") able to be controlled, at least to be stopped for the purpose of suspending the suction, independently of the main suction means, mould device characterised in that the second mould part comprises at least one hollow moulded part, the said part being arranged in a way to be located, when the mould is closed, directly facing the or each specific limited section respectively of the work area of the first mould part, and in that the or each hollow moulded part is movable in translation, preferably according to a direction substantially perpendicular to the work area of the second mould part or on a plane which is locally tangential to the said work area, the said part being advantageously mounted in an interchangeable manner on the said second mould part.