This paper examines the problem of shape based object recognition and proposes an approach to it based on certain characteristic planes of an object. It deals with a certain class of 3-D objects and their shapes. A shape distance for such objects is proposed on the basis of which shape discrimination between 3-D objects is possible. Two objects have the same shape if and only if one is a translation, dilation and rotation of the other. Thus, for shape matching, an object has to be normalized in terms of its position, size and orientation. Normalization of an object in terms of its position and size can easily be achieved. The main problem in shape matching involves normalization of orientation of an object. Here this problem is solved by using certain characteristic planes of an object. Thus, in order to compare shapes of two 3-D objects, first their position and volume are normalized. Then after normalizing their 3-dimensional orientation using the characteristic planes, they are superimposed on each other. The resulting volume of mismatch is taken to be a shape distance between the two objects. In the analog domain, this shape distance satisfies all the four metric properties.