In finite-difference time-domain (FDTD) modeling of elastic waves, absorbing boundary conditions are used to mitigate undesired reflections that can arise at the model's truncation boundaries. The perfectly matched layer (PML) is generally considered to be the best available absorbing boundary condition. An important but rarely addressed limitation of current PML implementations is that their performance is severely reduced when waves are incident on the PML interface at near-grazing angles. In addition, very low frequency waves as well as evanescent waves could cause spurious reflections at the PML interface. In electromagnetic modeling, similar problems are circumvented by using a complex frequency-shifted stretching function in the PML formulas. However, in elastic-wave modeling using the conventional PML formulation — based on splitting the velocityand stressfields — it is difficult to adopt a complex frequency-shifted stretching function. We present an alternative implemen-tation of a PML that is based on recursive integration and does not require splitting of the velocity and stress fields. Modeling re-sults show that the performance of our implementation using a standard stretching function is identical to that of the convention-al split-field PML. Then we show that the new PML can be modi-fied easily to include the complex frequency-shifted stretching function. Results of models with an elongated domain show that this modification can substantially improve the performance of the PML boundary condition. An efficient implementation of the new PML requires less memory than the conventional split-field PML, and, therefore, is a very attractive alternative to the con-ventional PML. By adopting the complex frequency-shifted stretching function, the PML can accommodate a wide variety of model problems, and hence it is more generic.