This paper presents the mechanical design for an anthropomorphic prosthetic hand which is one of the main components of an upper limb prosthesis. The design includes the pathways for the finger flexing cables which can be actuated using shape memory alloy (SMA) wires. Two prototypes were implemented and evaluated. The second prototype showed advantages of improved grasping capabilities and a more natural shape of the fingers. The design is based on simple mechanisms which can be incorporated in the limited space available. It utilizes fewer cables for finger flexion thus requiring fewer control inputs and simplifies the required control scheme. This results in a hand which is more affordable, lighter in weight, easy to control and requiring less power consumption.