The real system under consideration comprises of a solidifying casting with the casting mould, environment and other external influences. The process observed begins with the introduction of liquid metal to the channels of the runner system and filling of the mould cavity. This is connected with the contact of liquid metal with the atmosphere and also, with the walls of the mould. During the filling of the mould cavity heat transfer between the metal surface and the walls of the mould takes place (by radiation and conduction), which in practice can lead to mould cracking, and next to the formation of casting surface defects. In this stage of the process of great significance are the hydrodynamic conditions. These are dependent on the metal itself (its viscosity), and also on the runner system (rate of flow, resistances). During this time in the volume of the casting and mould, a pseudo-initial temperature fields is generated which is significant for the filling of the mould cavity and also for further cooling and solidification of the casting.