This cart has a capacity of 3,000 lbs. While I do not knw the weight of a 1936 Desoto Airstream body, I cannot imagine the body alone is 3,000 lbs. With that said, if you're concerned about the weight of the body, we'd recommend weighing it first before ordering the cart. Our specs say the cart is 'Adjustable width & length from 38' - 65' on either side' so we'd recommend looking underneath your car and making sure these dimensions from the cart will allow you to contact the car at your desired support positions. I hope this helps! Thanks for shopping with us Pete!