Resistive　random　access　memory　device　(RRAM)　has　been　widely　used　in　various　novel　circuit　systems,　such　as　memory,　artificial　intelligence,　and　neural　networks,　due　to　its　unique　memory　characteristics.　However,　there　are　very　few　studies　focusing　on　analytic　modeling　of　RRAM.　In　this　article,　modeling　for　solving　analytic　approximate　solution　to　the　state　variable　of　RRAM,　based　on　the　proposed　Multistage　Homotopy　Analysis　Method　(MuHAM),　is　proposed.　Different　from　traditional　HAM,　the　time　span　under　consideration　is　divided　into　many　subintervals,　then　the　convergence　control　parameter　in　each　subinterval　is　optimized　to　achieve　high　approximation　accuracy.　By　simulating　and　comparing　the　obtained　analytic　solutions　with　solutions　solved　by　other　traditional　homotopy-based　modeling　methodologies　and　by　numerical　analyses,　we　verified　that　MuHAM　has　higher　Quality　Factor　(introduced　to　evaluate　the　model　accuracy　and　computational　cost　comprehensively),　hence　improving　the　simulation　efficiency.　Besides　the　classical　Hewlett-Packard　(HP)　RRAM,　some　current　RRAMs　are　also　verified.　MuHAM　also　has　the　advantages　of　enabling　both　qualitative　and　quantitative　analyses,　and　immunity　to　convergence　issues.　It　is　particularly　suitable　for　the　analytic　modeling　of　the　other　novel　memory　devices　having　strong　nonlinearity.