Based on the model of finite compressible strata and boundary element method of Reissner’s plate beading problem

the modified integral equations and a general numerical method on the interaction of raft foundations with the finite compressible strata are presented

in which the shape of columns loading and the effect of transverse shear deformation in the raft are considered. For elastic half-space model

the flexibility equations can be obtained by regarding as a special case of the finite compressible strata model. The raft is treated as thick plate with free edge boundary conditions

and is discretized by a series of triangular or rectangular domain cells or elements

the subgrade reaction is assumed as uniformly distribution in each cell

and thus is consistent with the computing settlement methods now. The numerical results show that the excessively high computing values of the subgrade reaction on the edges of raft are avoided by using the discontinuous bearing pressure distribution at cell conjunctions

which have little influence on the computing results. The presented numerical results

which use finite compressible strata model and elastic half-space model respectively

are compared with those previous researchers. It is shown that higher accurate results can be obtained even with a few numbers of boundary elements and internal cells for practical complex raft foundation.