If you're wanting to make them billowed out as it would be if the paratrooper/fallschirmjager were in the air "fallin' from the sky," or just after landing then I'd say make a thin wire frame for the chute where the shroud lines would be, then add tissue paper or facial tissue over that for the silk. Stiffen the "chute" with a thinned white glue solution and let dry before painting. Use string or thread for the shroud lines themselves. Do an image search online for parachutes or paratroopers and see how the deployed 'chutes look and how the rigging attaches to the 'trooper's harness.
If you're talking about making parachute packs for figures, then putty or some other moldable, sculptable material would be the best choice.