We present a novel parametric 3D shape representation, Generalized sum of Gaussians (G-SoG), which is particularly suitable for pose estimation of articulated objects. Compared with the original sum-of-Gaussians (SoG), G-SoG can handle both isotropic and anisotropic Gaussians, leading to a more flexible and adaptable shape representation yet with much fewer anisotropic Gaussians involved. An articulated shape template can be developed by embedding G-SoG in a tree-structured skeleton model to represent an articulated object. We further derive a differentiable similarity function between G-SoG (the template) and SoG (observed data) that can be optimized analytically for efficient pose estimation. The experimental results on a standard human pose estimation dataset show the effectiveness and advantages of G-SoG over the original SoG as well as the promise compared with the recent algorithms that use more complicated shape models.