In this paper, we describe a statistical shape analysis founded on a robust elastic metric. The proposed metric is based on geodesics in the shape space. Using this distance, we formulate a variational setting to estimate intrinsic mean shape viewed as the perfect pattern to represent a set of given shapes. By applying a geodesic-based shape warping, we generate a principal component analysis (PCA) able to capture nonlinear shape variability. Indeed, the proposed approach better reflects the main modes of variability of the data. So, characterizing dominant modes of individual shape variations is conducted well through the reconstruction process. We demonstrate the efficiency of our approach with an application on a GESTURES database.