A tamponade catheter is disclosed for controlling bleeding from a penetrating or perforating wound in a patient comprising a catheter having an inner catheter lumen with a non-elastic inflatable balloon secured to the catheter in fluid communication with an inner catheter lumen of the catheter. A removable outer sheath overlays the inflatable balloon for inserting the inflatable balloon within the wound of the patient. A bendable flexible stiffening stylet is receivable within the inner catheter lumen of the catheter to aid in navigating the catheter into the wound of the patient. The removable outer sheath and the stylet are removable for inflating the inflatable balloon by an introduction of a fluid through the inner catheter lumen of the catheter for enabling the inflated non-elastic inflatable balloon to create pressure within the wound of the patient to control bleeding therefrom.