The invention relates to a novel, innovative industrial method for producing polystyrene (EPS) foam parts of arbitrary length and having a constant cross-section, with mixed densities located in accordance with the mechanical and thermal properties required for each application. The invention also relates to a machine (apparatus) for producing said solid parts having localized densities defined by the mechanical and thermal requirements of the application. The aforementioned products are produced by joined both longitudinally and transversely. The invention can be used to reduce the standard method to three steps, thereby resulting in a significant saving in terms of production. Moreover, unlike with the standard method, variants can be produced using the above-mentioned method, thereby increasing the range of application said type of products.