The introduction of an "incubation time" to the Schwarz classical mathematical description of metals solidification, resulted in a new model called Modified Schwarz Model. By doing so it was possible to identify and quantify the "delay time" that separates the two heat waves traveling independently in a casting during the solidification: the Supercooled / Superheated Liquid and the Solid / Liquid. The thermal shock produced in the initial stage of the undercooling generation process, can be used as an important parameter in the forecasting of the solidification's behavior of pure metals and alloys, when changing mold's materials, pouring and ambient temperatures. The hypercooling proneness degree of metals and alloys, can also be calculated.