This thesis describes and evaluates approaches to computational models of Epithelial cell interactions. It begins with a review of existing approaches and in particular includes a rational reconstruction of a model of squamous epithelial cell interactions previously described by Stekel Stekel et al., 1995 . Suggestions for improving this model are made, including methods for analysing spatial clusters of cells using Delau- nay triangulation and heterogeneity of epithelial tissue using connective component labeling. Histological images of oral epithelium are used to develop a classification of base ment membrane shape in normal and dysplastic tissues. The method combines Fourier descriptors for shape representation, Principal Component Analysis for data reduction and the closest mean and support vector machine algorithms for pattern recognition. This approach is suggested as a general technique for evaluating the output of simulation models which involve curvilinear features in a shape-based clas sification of the tissues modelled. A new model of epithelial cell interactions is proposed by extending the Glazier- Graner framework for cell sorting Graner, 1993, Graner and Sawada, 1993 . The model includes biological processes such as cell division, differentiation, adhesion and death. In particular, the roles of differential adhesion and cell division during the-development of epithelium are discussed. The typical ordered structure of a healthy epithelium is shown to arise provided differential adhesion and cell division are modelled appropriately.