Investigating　the　constitutive　relationship　and　the　damage　failure　mechanism　of　solid　propellants　is　of　significance　for　improving　the　safety,　storage　period　and　use　efficiency　of　solid　rocket　motors.　This　paper　focuses　on　the　complex　mechanical　response　behavior　of　composite　solid　propellants　under　loads　and　introduces　experimental　research　on　quasi-static　and　dynamic　mechanical　properties.　Limited　by　the　accuracy　of　instruments　and　testing　methods,　the　research　progress　of　macroscopic　constitutive　models,　mesoscopic　mechanical　models　and　microscopic　molecular　models　is　summarized　from　the　perspective　of　numerical　simulations　based　on　model　scale　and　modeling　methods.　This　paper　tracks　the　historical　progress　of　key　models　and　summarizes　the　main　achievements　and　prospects　in　this　field.　The　research　in　this　paper　has　high　scientific　and　theoretical　significance　and　engineering　application　value.　It　can　provide　an　important　reference　and　guidance　for　the　structural　optimization　and　performance　improvement　of　solid　propellants　and　lay　a　solid　foundation　for　the　development　of　solid　rocket　motors.　©　2023　by　the　authors.