A technique for the aeroelastic solution of parachute decelerators is presented in this work. The methodology uses empirical aerodynamics, based on a filling-time inflation model and Ludtke's area law, coupled to two explicit structural solution approaches. A mass-spring-damper technique allows solving the deployment of the system (when the grid is highly distorted) efficiently, and a finite element model is used for the accurate calculation of the structural loads and stresses during parachute opening and steady flight. The coupling strategy is staggered and the models share the same mesh. The methodology is intended for practical calculations of deceleration systems, and provides useful performance and structural data minimizing model complexity and computational cost. The suitability of the proposed technique is assessed by comparisons with reference test drop data.