A hybrid model for radiation from a borehole while drilling has been developed. A numerical model for propagation in a borehole including a drill pipe has been combined with the OASES frequency--wave-number model for propagation in layered earth media, using the concept of effective sources. Equivalent line source arrays that produce the same far-field radiation as the borehole are first computed. These are then introduced into the layered earth model and the resultant seismic wave field is computed. The borehole modes are excited by a displacement source at the bottom, simulating bit motion while drilling. In contrast to earlier work the present model includes the drill pipe in the simulation, allowing for three propagating modes at low frequencies. The model has been applied to analysis of the role of the formation composition in the radiation from the tube modes. The fundamental differences between the radiation into soft and hard formations are discussed and demonstrated, including the formation of Mach cones along the borehole in soft formations.