Abstract: It is,so far,difficult to simulate on computers with FEM the solidification processes and to propose their mathematical models describing the interdentric flow in liquid state if the density changes caused by the solidification shrinkage are taken into account.In this paper,a set of equations comprising mass,momentum and energy has been put forward on the principle of conservation of microelements in solid and liquid states,given a variable A and its relation to the velocity known.During calculation,this set of equations is used to deal with the liquid state,solid state and the solid-liquid state.Having cancelled the differentials of the products of the field quantity density and the field quantity velocity(or temperature),these partial differential equations are applicable to the computer-aided FEM simulation of the unstable time-dependent so-lidification processes in consideration of solidification shrinkage and the interdentric flow in liquid state.