We develop a modified Youngs interface reconstruction algorithm for Eulerian muhi-material hydrodynamic numerical methods. In the algorithm, the material's volume fractions of surrounding cells are used not only to calculate position of the interface but also to determine the transportation priority of materials. In a two dimensional muhi-material Eulerian hydrocode MMIC-2D, the algorithm is employed and validated in simulation of a cirque moving in a translational flow field in two dimensional Descartes coordinates. In the simulation of jet formation of shaped charge, material interfaces are clearly shown and agree well with experimental resuhs. It demonstrates accuracy and efficiency of the modified Youngs interface reconstruction algorithm.