The algorithm proposed here can be used in 2D two-step plane and axisymmetric Eulerian hydrodynamic method to deal with the interface of a mixed cell. It takes advantage of the idea of Youngs method: in a mixed cell, the interface is regarded as a straight line. The area fraction of eight cells surrounding the mixed cell is used to determine the normal orientation of the interface, the area fraction or the volume fraction of the mixed cell is used to determine the equation (position) of the interface, and then the flux passing across the boundary of the cell according to this interface and the area fraction or the volume fraction of the cell at next time is calculated. In the last part of this report, some numerical results are presented, which include the precision tests of interface calculation, the comparison with SLIC and the calculations of comprehensive problems.