Determining the optimum configuration of a mechanical hand in order to grasp an object is a computational hard work, mainly due to the large number of degrees of freedom (fingers and wrist), the existence of a large number of solutions, and the constraints imposed by the object or the task to be done. This paper presents an approach to solve this problem under certain conditions, which is then particularized for an anthropomorphic mechanical hand involving 22 degrees of freedom. The configurations of the hand to optimally grasp rectangular parallelepipeds of different sizes with a planar grasp (contact points on the same plane) are determined off-line from the results the wrist position is analyzed and stored as approximated functions of the height and width of the grasped object. This information is used for a fast on-line computation of the hand configuration in a real grasp operation, given the rectangular parallelepiped bounding-box of the part of the object that will be “inside” the hand after the grasp. The approach has been implemented for the mechanical hand MA-I and the paper includes numerical examples.