In the present paper, a model of an underactuated robotic hand with tendon driven fingers is proposed. The aim of the project was to study the feasibility of building a mechanical hand with four or five fingers, the movement of which is achieved using a single linear actuator. The mechanism was first modelled in order to study the possible improvement in the ability of a “robotic hand” powered with a single actuator in regard to grasping objects with complex shapes and also in achieving a strong grip on objects. Next, a model of the finger was studied in order to optimize of its parameters. Finally, a five-fingered robotic hand was modelled for potential application as a human hand prosthesis. Our studies on the dynamic and kinematic behaviour of a single finger mechanism permitted us to make the first prototypes of the mechanism. In addition to modelling studies, we also present a prototype of the modelled robotic hand that was developed in order to optimize functionality and simplicity of construction.