Shape analysis is a timely and interesting research field.  In this work, assuming that it is possible to extract from the shape a finite number of representing points, called landmarks, each landmark is modeled with a bivariate Gaussian distribution in which averages are geometric coordinates and variances take into account the shapes variability and measurement errors. The Fisher-Rao metric is then used as a Riemannian metric of the statistical model thus identified. Consequently, geodesic paths can be computed as locally minimizing distances in the Fisher information sense. The methodology enables to perform various types of analysis including shape comparisons, interpolation between observed shapes and shape predictions.  In particular, the length of the geodesic path connecting two shapes can be used for quantifying shape differences and used in a cluster analysis of shapes.