This paper is concerned with computer simulation of concurrent grasp and orientation control of an object with two parallel flat surfaces by a pair of multi-degrees of freedom robot fingers that have rigid hemispherical ends. Firstly, geometrical relationships in the overall fingers-object system are discussed through four algebraic constraints between the finger tips and surfaces of the object. Then, differential algebraic equations expressing dynamics of the overall system are derived. Secondly, a sensory feedback signal for concurrent grasp and orientation control of the object is proposed and a full description of matrix form for numerically solving the closed-loop differential algebraic equation of the overall fingers-object system on the basis of the CSM (constraint stabilization method) is presented. Thirdly, simulation results of grasping and orientation control of the object are shown and then, the effects of each term of the proposed control input signal on the system performances are discussed. Finally, a guidance of gain tuning is suggested on the basis of well-known force-velocity characteristics of human muscle in muscle physiology.