This paper deals with an analysis of the compliance characteristic for effective peg-in-hole task using robot hand without inter-finger coupling. We first observe the fact that some of coupling stiffness elements cannot be planned arbitrary. next we classify the task of inserting a peg-in-a-hole into two contact styles between the peg and the hole. Then we analyze the conditions of the specified stiffness matrix in the operational space to successfully and more effectively achieve the give peg-in-hole task for each case. It is concluded that the location of compliance center on the peg and the coupling stiffness element existing between the translational and the rotational direction play important roles for successful peg-in-hole task. Simulation results are included to verify the feasibility of the analytic results.