Flexible high-pressure angioplasty balloons are disclosed herein which utilize an inflatable balloon positioned upon the catheter and a supporting structure secured over or along the catheter at a first location proximal to the balloon and at a second location distal to the balloon. Inflation of the balloon reconfigures the supporting structure to urge the first location and the second location towards one another thereby inhibiting longitudinal elongation of the balloon relative to the catheter. The supporting structure may surround, support, or otherwise extend over the entire length of the balloon and allows for the balloon to retain increased flexibility which enables the balloon to bend or curve even at relatively high inflation pressures.