<p>The present work reports a numerical simulation on transport phenomena during laser welding of dissimilar materials (Ti–6Al–4V and AISI 316L). Laser welding involves simultaneous melting and solidification during the processing of materials in the presence of a high-energy density laser beam. The process is modelled based on the conservation equations of mass, momentum and energy. A FORTRAN code based on the finite volume method is developed for the present study. It initially presents the distribution of temperature and tracking of the solid–liquid interface under a stationary laser beam and comes out with a limit of the travelling speed of the laser beam beyond which full penetration is not feasible. At different values of travelling speed, the simulation predicts an eggplant-shaped weld pool behind the moving laser beam in considering simultaneous melting and solidification processes. Consideration of simultaneous melting and solidification under a moving laser beam results in an eggplant shape of weld pool, which is the novelty of the present work. The shape of the weld pool is smaller in the AISI 316L side than that of Ti–6Al–4V side due to the density difference of the alloys. It is found that the size of the weld pool, depth of penetration and heat-affected zone (HAZ) increase with an increase in the value of laser power and decrease with an increase in the value of travelling speed of the laser beam.</p>