Dynamic behaviour of parachutes is highly complex and characterised by non-linear, time dependant Fluid Structure Interaction, which is computationally intensive and hence not a viable option for incorporating into trajectory simulations. The paper describes modelling of ”Computationally efficient, High Fidelity Multi-Body” Parachute - Elastic Riser - Payload system, capable of simulating trajectory from parachute deployment to parachute separation. The differential equations of motion, including the kinematical and kinetic relationships are derived using the matrix form of Kane’s method, which avoids the typical complexity involved in symbolic derivations, available in published literature.The developed model is validated with published literature results formulated using Newton Euler method and simulation results demonstrating the typical characteristic motion of the system during descend are presented.