This paper details a procedure for classifying facial expressions. This is a growing and relatively new type of problem within computer vision. One of the fundamental problems when classifying facial expressions in previous approaches is the lack of a consistent method of measuring expression. This paper solves this problem by the computation of the Facial Expression Shape Model (FESM). This statistical model of facial expression is based on an anatomical analysis of facial expression called the Facial Action Coding System (FACS). We use the term Action Unit (AU) to describe a movement of one or more muscles of the face and all expressions can be described using the AlTs described by FACS. The shape model is calculated by marking the face with 122 landmark points. We use Principal Component Analysis (PCA) to analyse how the landmark points move with respect to each other and to lower the dimensionality of the problem. Using the FESM in conjunction with Support Vector Machines (SVM) we classify facial expressions. SVMs are a powerful machine learning technique based on optimisation theory. This project is largely concerned with statistical models, machine learning techniques and psychological tools used in the classification of facial expression. This holistic approach to expression classification provides a means for a level of interaction with a computer that is a significant step forward in human-computer interaction.