A new method for computing transient wave fields in a stack of liquid layers overlying a solid elastic layered half-space is presented. By taking the frequency, ω, and wavenumber, k, simultaneously as complex variables and choosing appropriate paths of integration in the ω-plane, the integration with respect to k in the well-known integrals representing the exact solution is performed exactly using Cauchy residue theory. The remaining integration (with respect to ω) is then performed approximately by use of the Fast Fourier transform and by other numerical integration methods. The theoretical results derived show that the complete wave field, including all possible body waves, can be represented simply as a superposition of modes. The method is easy to apply and computationally efficient, and is valid for both near- and far-field solutions. The same method is also applicable to axisymmetric borehole problems. The application of the method is illustrated in detail with a numerical example.