A balloon catheter for use in angioplasty and the like includes a shaft made of an elastomeric tube reinforced with longitudinally inelastic filaments. In the distal balloon portion of the unpressurized shaft, the filaments lie at an angle which is less than a predetermined critical angle. In the adjacent movable portion of the shaft, the filaments lie at an angle which is greater than the critical angle. When the shaft is pressurized, the balloon portion expands in diameter and the balloon portion contracts in diameter until the filaments in each portion lie at the critical angle. At the same time, the length of the movable portion increases so as to offset the reduction in length of the balloon portion.