Non-isothermal　three-variable　autocatalytic　chemical　kinetic　model　that　describes　the　reaction　mechanism　of　solid　phase　chemical　reaction　systems　is　presented　in　this　paper.　It　can　be　seen　from　the　numerical　solutions　that　the　oscillatory　combustion　occurs　mainly　as　a　result　of　competing　reactions　among　the　three　phases　of　reducing　agent　with　oxygen.　The　periodic　oscillatory　phenomena　and　multi-steady-state　solutions　adapted　to　demands　could　be　obtained　for　the　appropriate　control　parameter　μ,　λ,　κ,　and　ε　in　the　calculation,　namely　the　oxidant,　frequency-formulating　species　and　reducing　agents　of　the　oscillatory　combustion　formulas　and　the　activation　energy　of　the　reaction　should　be　selected　suitably　in　order　to　generate　oscillatory　combustion.　The　numerical　analysis　results　enrich　the　study　of　nonlinear　chemical　kinetic　model.