Landing parachute systems are among the most demanded samples of parachute equipment. The purpose of the study was to find new principles for developing parachutes with increased stability according to the analysis of the results of numerical and experimental studies of canopies of various shapes. The paper proposes to supplement a traditional definition of the stability of a parachute system with the obligatory consideration of the system’s ability to maintain a given trajectory of movement with a neutral canopy, regardless of the change in the payload mass. It is the expanded concept of stability that is taken as the basis of the modern approach to the design of foreign landing parachute systems. The study substantiates the main criteria for choosing the optimal cutting shape for parachute systems of increased stability of various types at the stage of preliminary design. The results of numerical modeling of canopies are presented: quarter-spherical, hemispherical, polyconic canopies and a T-11 type parachute canopy. Based on the analysis of these results, the study was first to propose a hypothesis that a decrease in the intensity of vortex formation in the wake leads to an increase in the stability of the parachute descent. The results of numerical modeling of canopies of various shapes, as well as experimental studies of a model polyconic parachute, which prove the correctness of the proposed hypothesis, are presented.