This paper deals with an analysis of the compliance characteristics for an effective peg-in-hole task using a robot hand without inter-finger coupling. We first classify the task of inserting peg-in-a-hole into three contact styles between the peg and the hole. Next, we analyze the conditions of the specified stiffness matrix in the operational space to successfully and more effectively achieve the given peg-in-hole task for each case. It is concluded that the location of the compliance center on the peg and the coupling stiffness elements between the translational and rotational directions play important roles for a successful peg-in-hole task. Simulation results are included to verify the feasibility of the analytic results.