A moulding method for making a monolithic component internally provided with at least one cavity, specifically a monolithic component made of C-SMC, comprising the following steps: - preparing a press comprising a first half mould and a second half mould, one between the first and the second half mould (1a, 1b) being moved by an oil circuit and the other between the first and the second half mould (1a, 1b) being stationary, the half moulds (1a, 1b) defining between them a moulding space (Vs), the press preferably also comprising movable side carriages acting in conjunction with the first and the second half mould (1a, 1b) to define the moulding space (Vs); - placing at least one core inside the moulding space (Vs), wherein the core (3, 4) comprises a membrane, delimiting a containing space (Vc) which is shaped to form the at least one cavity of the monolithic component, and at least one connector engaged with the membrane and configured to allow filling the containing space (Vc); - wrapping a charge of material to be moulded around the core (3, 4) so that the core (3, 4) is at least partly immersed in the charge; - fixing the core (3, 4) inside one between the first and the second half mould (1a, 1b), specifically the stationary half mould; - filling the containing space (Vc) of the membrane with a filling material through the connector; - after closing the half moulds (1a, 1b), applying a moulding pressure on the charge of material to form the monolithic component; and, after these steps, - emptying the containing space (Vc) of the filling material; - after opening the half moulds (1a, 1b), removing the core (3, 4) from the moulded monolithic component, in the method being characterized in that in the step of filling the containing space (Vc) of the membrane, the containing space (Vc) is placed in fluid communication with a delivery section of the oil circuit to allow creating a feed flow whereby a predetermined quantity of oil flows from the oil circuit to the containing space (Vc), and/or in that in the step of emptying the containing space (Vc), the containing space is placed in fluid communication with a return section of the oil circuit to allow creating a return flow whereby the predetermined quantity of oil flows back from the containing space to the oil circuit. - preparing a press comprising a first half mould and a second half mould, one between the first and the second half mould (1a, 1b) being moved by an oil circuit and the other between the first and the second half mould (1a, 1b) being stationary, the half moulds (1a, 1b) defining between them a moulding space (Vs), the press preferably also comprising movable side carriages acting in conjunction with the first and the second half mould (1a, 1b) to define the moulding space (Vs); - placing at least one core inside the moulding space (Vs), wherein the core (3, 4) comprises a membrane, delimiting a containing space (Vc) which is shaped to form the at least one cavity of the monolithic component, and at least one connector engaged with the membrane and configured to allow filling the containing space (Vc); - wrapping a charge of material to be moulded around the core (3, 4) so that the core (3, 4) is at least partly immersed in the charge; - fixing the core (3, 4) inside one between the first and the second half mould (1a, 1b), specifically the stationary half mould; - filling the containing space (Vc) of the membrane with a filling material through the connector; - after closing the half moulds (1a, 1b), applying a moulding pressure on the charge of material to form the monolithic component; and, after these steps, - emptying the containing space (Vc) of the filling material; - after opening the half moulds (1a, 1b), removing the core (3, 4) from the moulded monolithic component, in the method being characterized in that in the step of filling the containing space (Vc) of the membrane, the containing space (Vc) is placed in fluid communication with a delivery section of the oil circuit to allow creating a feed flow whereby a predetermined quantity of oil flows from the oil circuit to the containing space (Vc), and/or in that in the step of emptying the containing space (Vc), the containing space is placed in fluid communication with a return section of the oil circuit to allow creating a return flow whereby the predetermined quantity of oil flows back from the containing space to the oil circuit.