A fluid dynamics approach to modelling of fusion welding in titanium alloys is proposed. The model considers the temporal and spatial evolution of liquid metal/gas interface to capture the transient physical effects during the heat source–material interaction of a fusion welding process. Melting and vaporisation have been considered through simulation of all interfacial phenomena such as surface tension, Marangoni force and recoil pressure. The evolution of the metallic (solid and liquid) and gaseous phases which are induced by the process enables the formation of the keyhole, keyhole dynamics, and the fully developed weld pool geometry. This enables the likelihood of fluid flow-induced porosity to be predicted. These features are all a function of process parameters and formulated as time-dependent phenomena. The proposed modelling framework can be utilised as a simulation tool to further develop understanding of defect formation such as weld-induced porosity for a particular fusion welding application. The modelling results are qualitatively compared with available experimental information.