A mathematical model was built to describe the transportation phenomena and the freckle formation during the solidification process of multicomponent Ni-base superalloy.A set of expressions of coupling liquidus and solid fraction as well as multicomponent concentrations was determined based on the pseudobinary phase diagram.The numerical simulation of Ni-5.8%Al-15.2%Ta(mass fraction)alloy during the vertically unidirectional solidification was performed by this continuum model.The results show that the model is reasonable to describe the formation and evolution of freckle in superalloy ingot.Freckles were significantly induced by the density inversion due to the thermosolutal convection in front of the solid/liquid interface.The solute-rich liquid in the channel flows from mush into liquid.In order to maintain the mass equilibrium in the channels,the fresh liquid may penetrate via the mushy zone from pure liquid region.The plumes appearing at the preliminary solidification stage were unstable and tended to converge.The stable channel was formed at the prior grown solidification front after the plumes were submerged.