This paper presents a new method to compute enveloping grasps with a multi-fingered robotic hand. The method is guided by the idea that a good grasp should maximize the contact surface between the held object and the hand's palmar surface. Starting from a given hand pregrasp configuration, the proposed method finds the hand poses that maximize this surface similarity. We use a surface descriptor that is based on a geodesic measure and on a continuous representation of the surfaces, unlike previous shape matching methods that rely on the Euclidean distance and/or discrete representation (e.g. random point set). Using geodesic contours to describe local surfaces enables us to detect details such as a handle or a thin part. Once the surface matching returns a set of hand poses, sorted by similarity, a second step is performed to adjust the hand configuration with the purpose of eliminating penetration of the object. Lastly, the grasp stability is tested in order to definitely validate the candidate grasps.