Skeletons are at the core of 3D character animation. The goal of this work is to design a morphable model of 3D skeleton for four footed animals, controlled by a few intuitive parameters. This model enables the automatic generation of an animation skeleton, ready for character rigging, from a few simple measurements performed on the mesh of the quadruped to animate. Quadruped animals - usually mammals - share similar anatomical structures, but only a skilled animator can easily translate them into a simple skeleton convenient for animation. Our approach for constructing the morphable model thus builds on the statistical learning of reference skeletons designed by an expert animator. This raises the problems of coping with data that includes both translations and rotations, and of avoiding the accumulation of errors due to its hierarchical structure. Our solution relies on a quaternion representation for rotations and the use of a global frame for expressing the skeleton data. We then explore the dimensionality of the space of quadruped skeletons, which yields the extraction of three intuitive parameters for the morphable model, easily measurable on any 3D mesh of a quadruped. We evaluate our method by comparing the predicted skeletons with user-defined ones on one animal example that was not included into the learning database. We finally demonstrate the usability of the morphable skeleton model for animation.