Cells adhere to each other through the binding of cell adhesion molecules at the cell surface. This process, known as cell-cell adhesion, is fundamental in many areas of biology, including early embryo development, tissue homeostasis and tumour growth. Here \~e present a new continuum mathematical model of this phenomenon by considering · the movement of cells in response to the adhesive forces generated through binding. We demonstrate that the model predicts aggregative behaviour, characteristic of an adhesive cell population. Further, when extended to two cell populations, the model predicts cell sorting behaviour dependent on the strengths of adhesive bonds between cells. While cell sorting has been demonstrated previously with discrete approaches, we believe that this is the first continuous model to capture this behaviour. In the latter part of this work we apply the model of cell-cell adhesion to somitogenesis and tumour growth. In applying the model to somitogenesis we demonstrate that the model predicts somite formation under particular parameter constraints. We suggest that these parameter constraints may provide a means by which to test competing theories of the mechanisms responsible for somitogenesis. In applying the model to tumour growth and invasion we demonstrate that the model predicts that mutations which alter cells adhesive properties have a significant influence on tumour dynamics. In particular, the model predicts that irregular invasion patterns are the consequence of increased cell-matrix adhesion and an inhomogeneous host environment.