This chapter focuses on the numerical exploration of the thermal pouring stage of the AT weldingAluminothermic (AT) welding of rails, which includes crucible discharge and mould filling. The solid-liquid phase change phenomena and RANS \(k - \varepsilon \) equations are solved, as detailed in Chap 3. The shape of the melted rails obtained from the numerical simulations are compared to those from experiments. Moreover, the influence of pouring temperature on the shape of the melted rails within the mould post-pouring stage is studied. In the experiments described in Chap. 5, the melted rails within the mould post-pouring stage are obtained by employing a draining mechanism.