A method is disclosed for foaming objects (2) inside moulding units (4) that are conveyed along an advancement path (P) by means of distinct and separate conveying modules (M T1 , M T2 ) that define a first portion (T1) and a second portion (T2) of path (P). In the first portion (T1) the steps occur of advancing moulding units (4) in an open position, extracting already moulded objects (2), preparing moulding units (4) for the subsequent foaming cycles of further objects (2), dispensing of the reactive mixture. Along the second portion (T2) of path (P) the moulding units (4) are advanced in the closed position while a polymerisation and shape-stabilisation process of said foamed objects (2) occurs. The mixture dispensing step is followed by a closing and transferring step, in which each moulding unit (4) is closed whilst, simultaneously, it is transferred from the first portion (T1) to the second portion (T2) of path (P) by a transfer-closing carousel unit (U CT ). At the end of the polymerisation and shape-stabilisation process that occurs in the second portion (T2) of path, an opening and transfer step is provided, in which each moulding unit (4) is opened whilst, simultaneously, it is transferred from the second portion (T2) to the first portion (T1) of path by an opening-transfer carousel unit (U AT ). The corresponding apparatus for implementing this method is also disclosed.