This paper presents a Bayesian framework for 3D facial reconstruction. The framework iteratively deforms a generic face mesh to fit a set of range points representing a face. The generic mesh is generated from the extensive FRGC database of face images. The deformation process is conducted within a Bayesian framework and is driven by a Markov Chain Monte Carlo (MCMC) sampler which uses information from the likelihood and prior distributions of the generic face mesh. The paper presents results on the construction of a generic face model, the deformation framework and fitting results to both synthetic and real data. The results verify the effectiveness of the proposed technique, accurately deforming a generic face mesh to captured 3D data points of human faces.