An apparatus for molding a continuous foamed plastics element (2), such as a floor construction member of the type comprising a substantially parallelepipedic central body (3) and at least one lateral projection (5,6), includes a mold (13) comprising a forming chamber (13a) and a stabilization chamber (13b) defined between a bottom wall (22), a pair of opposite side walls (20,21), and a cover (23). Advantageously, the cover (23) and/or one or both the side walls (20,21) of the mold (13) comprise a plurality of structurally independent segments which may be adjustably positioned toward and away from the bottom wall (22) of the mold (13) for independently adjusting, in a substantially continuous manner, the height of the molding seats of the central body (3) and/or of the lateral projection (5,6) of the continuous element (2) in each of the forming (13a) and stabilization (13b) chambers of the mold (13).