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We construct the solutions to the Riemann problem for the isentropic extended Chaplygin gas dynamic system for all kinds of situations by the phase plane analysis. We investigate the asymptotic limits of solutions to this problem in detail when the pressure given by the state equation of the system becomes the one of pressureless gas. During the process of vanishing pressure, the two-shock Riemann solution tends to a delta shock solution, whereas the two-rarefaction-wave Riemann solution tends to a two-contact-discontinuity solution with a vacuum state.

The asymptotic limits of Riemann solutions for the isentropic extended Chaplygin gas dynamic system with the vanishing pressure