Generalized cylinders model uses hierarchies of cylinder-like modeling primitives to describe shapes. It captures many of our intuitions about axes of symmetry and hierarchical description. The axes of symmetry form the skeleton of the shape. A generalized cylinder is a surface created by moving a cross section along an axis. The axis is a space curve and the cross section can be transformed by rotation, scaling, or distortion during the motion. We would like to give a natural and intuitive definition of axis for cylindrical shapes. For 2D shapes, the medial axis is a good candidate, though it is sensitive to perturbations. For 3D shapes, the medial scaffold is often complicated surfaces and does not match people's intuitions very well. We give a new definition of axis for generalized cylinders based on principal curves. This approach uses a regression point of view, defining the axis as a minimization point of a energy function. We prove the existence of a solution and give the equations of the minimization point. We also apply the definition to some real and artificial examples and get good results. Our goal is to produce natural and intuitive shape descriptions for 2D and 3D shapes. We believe that is essential for building general objects recognition systems. It would be also useful in shape analysis, classification and compression.