A catheter for crossing an occluding lesion with an inflatable balloon and dilating the lesion includes an inner tube that defines a longitudinal axis. The balloon includes a distal section that is bonded to the tube's distal end, a working section, and a conically shaped distal transition section connecting the working and distal section. A plurality of rigid ribs are spaced around the circumference of the balloon near the catheter's distal end. Each rib includes a first elongated portion attached to the balloon's distal section and aligned substantially parallel with the longitudinal axis. A second portion extending from the first portion and at an angle thereto is attached to and lies along the surface of the balloon's distal transition section. The plurality of ribs combine to simulate a stiff, tapered surface that can be wedged into the occluding lesion to create a passageway to cross the lesion with the balloon.