A patient restraining device is secured to a patient supporting structure, such as an ambulance cot, to more safely support a person's body during transport from one place to another. The device includes at least one sheet of fabric and connectors secured to the fabric. With the device fastened to an ambulance cot, either directly or via the ambulance cot mattress, a person is positioned on the cot mattress, and then the fabric is wrapped about the person's body, and the connectors are secured about the person's body. Among other things, the device may be used to stabilize the abdominal mass of a bariatric patient, and thereby safely increase the effective “patient capacity” of an otherwise conventional ambulance cot. When not in use, the device is stored in one or more storage cavities defined by the ambulance cot mattress.