Somitogenesis, the sequential formation of a periodic pattern along the antero-posterior axis of vertebrate embryos, is one of the most obvious examples of the segmental patterning processes that take place during embryogenesis and also one of the major unresolved events in developmental biology. In this article, we develop a mathematical formulation of a new version of the Clock and Wavefront model proposed by Pourquié and co-workers (Dubrulle, J., McGrew, M.J., Pourquié, O., 2001. FGF signalling controls somite boundary position and regulates segmentation clock control of spatiotemporal Hox gene activation. Cell 106, 219-232). Dynamic expression of FGF8 in the presomitic mesoderm constitutes the wavefront of determination which sweeps along the body axis interacting as it moves with the segmentation clock to gate cells into somites. We also show that the model can mimic the anomalies formed when progression of the wavefront is disturbed and make some experimental predictions that can be used to test the hypotheses underlying the model.