This thesis presents a new approximate theoretical analysis of pile-raft foundations from which a Direct Boundary Element Method (DBEM) computer code has been developed. It is assumed that, at the present time, linear elastic soil models provide a sufficient degree of sophistication for such an analysis. The analysis developed couples a 'plate-bending boundary element analysis' with that of a pile-reinforced supporting linear elastic continuum. A parametric study was carried out using PGroup 3.0 (the Department of Transport pile analysis computer program), which provided flexibilities for a single pile, pairs of piles, 3 pile group and square arrangements of 4, 9 and 16 piles (in an elastic soil with a modulus increasing linearly with depth) in a form useful to the pile designer. The study was also extended to develop empirical equations, using output from PGroup 3.0, to provide algebraic expressions for the vertical flexibility of single piles, which were then incorporated in the classically supported raft analysis to allow for the presence of piles beneath it. The author's computer program, based on the above model, has been thoroughly tested by comparing its predictions with both published analytical and numerical solutions and data obtained from field measurements on full-scale pile rafts.