This present research is concerned with the design, development and implementation of three-dimensional computer-generated facial images capable of expression gesture and speech. A review of previous work in chapter one shows that to date the model of computer-generated faces has been one in which construction and animation were not separated and which therefore possessed only a limited expressive range. It is argued in chapter two that the physical description of the face cannot be seen as originating from a single generic mould. Chapter three therefore describes data acquisition techniques employed in the computer generation of free-form surfaces which are applicable to three-dimensional faces. Expressions are the result of the distortion of the surface of the skin by the complex interactions of bone, muscle and skin. Chapter four demonstrates with static images and short animation sequences in video that a muscle model process algorithm can simulate the primary characteristics of the facial muscles. Three-dimensional speech synchronization was the most complex problem to achieve effectively. Chapter five describes two successful approaches: the direct mapping of mouth shapes in two dimensions to the model in three dimensions, and geometric distortions of the mouth created by the contraction of specified muscle combinations. Chapter six describes the implementation of software for this research and argues the case for a parametric approach. Chapter seven is concerned with the control of facial articulations and discusses a more biological approach to these. Finally chapter eight draws conclusions from the present research and suggests further extensions.