Abstract: Installing vertical drains between stone columns can provide more vertical drainage paths to accelerate the consolidation of soft soils. The faster consolidation of soils around columns provides the larger bearing capacity of a composite foundation. However, consolidation theories of the composite foundation considering two vertical drainage bodies have been rarely reported in the literature. As a result, its bearing capacity and settlement calculation is out of theories. On the basis of the study status, the composite foundation with vertical drains-stone columns was regarded as an object. The radial seepage of pore water in the soil around columns to two vertical drainage bodies and the vertical upward seepage were considered. Under the condition that the top surface of composite foundation is permeable and the bottom surface is impermeable, a consolidation model for the composite foundation with vertical drains-stone columns were developed according to the continuity condition of the flow volume among vertical drains, stone columns and soils, and an analytical solution for the consolidation model was derived. This analytical solution can be reduced to the analytical solution for the consolidation of composite foundations with stone columns by considering radial and vertical seepage and the consolidation of soils with classical vertical drains, respectively. Finally, the analytical solution is used to carry out a lot of analysis and calculation to investigate consolidation behaviors of this composite foundation. The results show that the consolidation rate of composite foundation greatly increases by installing vertical drains among stone columns. The smear effect of stone columns has great influences on the consolidation rate, but the smear effect of vertical drains has little influence on the consolidation rate. If vertical drains are installed among stone columns, only the radial seepage in soils around columns can be considered to accelerate the consolidation rate of soils.