Double-membrane gliding parachutes (DGP) obtain their wide variety of application, including the solution of cargo transportation problems. This parachute is a flexible canopy, which shape is maintained by ram air. In terms of the aerodynamic performance calculation and analysis when operating, DGP is the most complex aero elastic system. The computation of DPG aerodynamic performance is only possible, utilizing the methods of nonlinear aerodynamics and the nonlinear theory of elasticity methods.This paper investigates the aerodynamic characteristics of stable geometric shapes for various gliding parachutes, taking into account their dome shape both chord-wise and span-wise. Notably, the volumetric parachute profile is modeled by its median surface. The research, conducted by the authors, showed that such an aero elastic model of DGP allows you to obtain results that reflect correctly the qualitative effects of detached and free streamline flow. To solve the problem about the airflow over a gliding parachute, considering its canopy curvature, the method of discrete vortices with closed frames is employed, which allows you to calculate the paragliding wing aerodynamic performance within a wide range of angles of attack. There is also a possibility of flow separation simulation. The ideal incompressible liquid flow over the median surface of a stable shape for a double-membrane gliding parachute is regarded. The parachute fabric porosity is not analyzed, since the upper and lower DGP panels are made of either the low permeable or non-porous fabric. In the separated flow past, the aerodynamic coefficients are identified by time averaging to its large values after computing. The DGP aerodynamic performance computation results are given at a different value of its dome shape, as in the free streamline flow as in the flow separation. The computed coefficients, that allow us to consider the influence of canopy dome shape on its aerodynamic characteristics, are obtained. The proposed technique can be used for operational estimates of aerodynamic forces while designing and planning a pipe experiment.