A generalization of the technique of Tubman et al. (1984) allows the inclusion of intermediate fluid layers in the theoretical study of elastic wave propagation in a layered borehole. The number and location of fluid layers are arbitrary. The only restrictions are that the central cylinder is fluid and the outermost formation is solid. Synthetic full-waveform microseismograms in poorly bonded cased holes can be generated, allowing investigation of free pipe and cement sheathed pipe with no bond to the formation.If there is a fluid layer between the steel and the cement, the steel is free to ring. The first arrival in this situation is from the casing, even with an extremely thin fluid layer or microannulus. The amplitude and duration of the pipe signal depend upon the thickness of the fluid layer. While the first arrival is from the casing, the formation body-wave energy is present. The character of the waveform will vary as the formation parameters vary. If the duration of the steel arrival is small, it is possible to distinguish the formation P-wave arrival.If the fluid layer is between the cement and the formation, then the steel is well bonded to the cement but the cement is not bonded to the formation. In this case the thicknesses of the fluid and cement layers are important in determining the nature of the first arrival. If there is a large amount of cement bonded to the steel, the cement can damp out the ringing of the pipe and make it possible to distinguish formation arrivals.If there is less cement bonded to the steel, the cement does not damp out the steel ringing but the cement rings along with the steel and the first arrival is from the combination of the steel and the cement. The velocity of this wave depends upon the velocities and thicknesses of the steel and cement layers.