A system of shuttle cars for transporting a vehicle in an automated parking facility. Each shuttle car includes an x-shuttle that supports two z-shuttles. The z-shuttles move from the x-shuttle and under the vehicle for transport. The z-shuttles locate and engage the front and rear tires of a vehicle to lift the vehicle from the floor. Once the z-shuttles have engage the vehicle tires, the z-shuttles return to the x-shuttle so that the x-shuttle can transport the vehicle (and the z-shuttles) to and from the appropriate parking space.