The hybrid rocket motors (HRM) use a two-phase propellant system. This offers some remarkable advantages but also arises some difficulties like the neutralization of their instabilities. The non-acoustic combustion instabilities are high-amplitude pressure oscillations that have too low frequencies to be associated with acoustics. Acoustic type combustion instabilities are self-excited oscillations generated by the interaction between acoustic waves and combustion. The goal of the present work is to develop a simplified model of the coupling of the hybrid combustion process with the complete unsteady flow, starting from the combustion port and ending with the nozzle. This model must be useful for transient and stability analysis and also for scaling of HRMs. The numerical results obtained with our model show a good agreement with published experimental and numerical results. The computational and stability analysis models developed in this work are simple, computationally efficient and offer the advantage of taking into account a large number of functional and constructive parameters that are used by the engineers.