Transient waveforms have been computed for a family of source and receiver types and for geometry corresponding to plausible acoustic logging tools in oil wells. The acoustic tool now in commercial use is one member of the family. The computations also treat flexural waves and torsional waves. All quantities are expressed in terms of appropriate vector and scalar potentials, and output waveforms are obtained by numerical evaluation of triple Fourier transforms. When loss parameters are included in the stress-strain relations, the Fourier inversion formulas are free of singularities and numerical integration is straightforward. For the purely elastic case, it is necessary to cope with the singularities of the integrands in performing the numerical integrations. Dispersion curves and other features agree with earlier publications on wave propagation along concentric cylinders.