In　this　paper,　we　study　the　formation　of　delta　shock　waves　and　vacuum　states　in　a　pressureless　limit　of　solutions　to　the　Euler　equations　of　compressible　fluid　flow　for　modified　Chaplygin　gas　as　two　parameters　tend　to　zero.　At　first,　the　Riemann　problem　of　Euler　equations　of　compressible　fluid　flow　for　modified　Chaplygin　gas　is　solved.　Then,　as　the　pressure　drops　to　zero,　we　strictly　confirm　that　the　two-shock　Riemann　solution　converges　to　a　delta　shock　wave　solution　and　the　two-rarefaction　wave　Riemann　solution　converges　to　a　two-contact　discontinuity　solution　with　the　intermediate　state　approaching　a　vacuum　state.　At　last,　some　numerical　simulations　are　given　to　verify　the　above　analysis.