This paper addresses the problem of grasp capability analysis of multifingered robot hands. The aim of the grasp capability analysis is to find the maximum external wrench that the multifingered robot hands can withstand, which is an important criterion in the evaluation of robotic systems. The study of grasp capability provides a basis for the task planning of force control of multifingered robot hands. For a given multifingered hand geometry, the grasp capability depends on the joint driving torque limits, grasp configuration, contact model and so on. A systematic method of the grasp capability analysis, which is in fact a constrained optimization algorithm, is presented. In this optimization, the optimality criterion is the maximum external wrench, and the constraints include the equality constraints and the inequality constraints. The equality constraints are for the grasp to balance the given external wrench, and the inequality constraints are to prevent the slippage of fingertips, the overload of joint actuators, the excessive forces over the physical limits of the object, etc. The advantages of this method are the ability to accommodate diverse areas such as multiple robot arms, intelligent fixtures and so on. The effectiveness of the proposed method is confirmed wit]~ a numerical example of a trifingered grasp.