In this paper, an analytical approach is proposed for planning finger positions of an object with multifingered hand. At first, a method is given to obtain which combination of the object edges ispossible to be usedfor gmsping. Then, Graspable Finger Position Region (GFPR) on a combination of edges is defined where the object can be held successfully. It is shown that the region is bounded by several bounday hyperplanes. With the combining these bounday hyperplanes, two propositions for analytically and exactly obtaining the GFPR am proposed. And, an algorithm is proposed to find the Stable GFPR that contains the biggest inscribed hypersphere of GFPR and has the larger volume. Lastly, numerical example is performed to show the effectiveness of the proposed grasp planning approach.