Abstract: The two-dimensional Riemann problem with initial data of two constant states for isentropic Chaplygin gas dynamic system is studied in the paper.Using plane wave and characteristic analysis methods,under the suitable generalized Rankine-Hugoniot relation and entropy condition,five kinds of plane wave solutions to the Riemann problem are constructed,which are composed of back(forward) rarefaction wave,back(forward) shock wave,contact discontinuity and -shock wave.