An explicit dynamic structural solver developed at CIMNE for the analysis of parachutes is presented. The canopy fabric has a negligible out-of-plane stiffness, therefore its numerical study presents important challenges. Both the large changes in geometry and the statically indeterminate character of the system are problematic from the numerical point of view. This report covers the reasons behind the particular choice of solution scheme as well as a detailed description of the underlying algorithm. Both the theoretical foundations of the method and details of implementation aiming at improving computational efficiency are given. Benchmark cases to assess the accuracy of the solution as well as examples of practical application showing the performance of the code are finally presented.