A modified ignition and growth(I&G) model which is necessary to simulate the combustion phenomena of energetic materials and an analytical model determining the unknown parameters of the reaction rate equation are proposed. The modified I&G model sustains important physical implications with overcoming some problems of previous rate equations. This rate model consists of ignition term which represents the formation of the hotspot due to void collapse and growth term which means the shock to detonation transition phenomena. Also, the theoretical model is used to investigate the combustion characteristics of certain energetic materials before running Hydrocode by pre-determination of unknown parameter, $b,;G,;x,;I$. The analytical model provides efficient and highly accurate results rather than previous method which simulated the unconfined-rate-stick via the numerical means.