Inflating a parachute is a complex process where the ballistics of the mechanical system involving the object and the parachute interact with the unsteady aerodynamics of large masses of air. This interaction is further influenced by the elastic properties of the textile materials used in the parachute’s construction. The primary challenge in parachute design is the inflation process. The goal of this work is to develop a method for calculating the force during parachute inflation based on generalizing the fundamental principles for determining the trajectory parameters of the system and considering its mechanical properties under impact loads. The work provides a brief analysis of the ballistics of the mechanical system, treating the object-parachute as a material point. Based on this, a method for calculating the maximum force during parachute inflation is presented. This method combines an integral approach for determining the effective speed of the system during parachute inflation and a technique for assessing the dynamic coefficient of the parachute system, taking into account the pliability of its construction. The validity of the proposed model, which considers the pliability of the construction, is confirmed through comparisons with the work of other authors.