Accurate estimation of the shape of human faces has many applications from computer-imaging to psychological research. One well known method is to fit a Three Dimensional Morphable Model to a target image. This method is attractive as the faces it constructs are already projected onto an orthogonal basis making further manipulation and analysis easier. So far its use in these fields has been limited the inaccuracy and inconvenience of current face-fitting methods. We present a method based on Genetic Algorithms that avoid the local minima and gradient image errors that current methods suffer from. It has the added advantage of requiring no manual interaction to initialise or guide the fitting process.