This article presents a method for building a mathematical model to determine the working parameters of a solid-fuel rocket engine. By changing some structural parameters around the initial values, the working characteristics of the rocket engine were investigated to evaluate the reliability of the designed structural parameters. The C5K solid-fuel rocket engine was selected to verify the model. The survey results show that: the volume of the combustion chamber increases by 20%, pressure decreases by 1.07%, thrust decreases by 1.07%, and engine working time increases by 2.9%. In addition, the change in critical cross-sectional diameter and the length of the propellant rod also significantly affects the thrust and working time of the engine. The results of the article are used as a theoretical basis to calculate and design rocket engines to ensure high accuracy.