New processors are increasingly supporting half-precision floating-point numbers, often with a significant throughput gain over single-precision operations. Seismic modeling, imaging, and inversion could benefit from such an acceleration, but it is not obvious how the accuracy of the solution can be preserved with a very narrow 16-bit representation. By scaling the finite-difference expression of the isotropic elastic wave equation, we have found that a stable solution can be obtained despite the very narrow dynamic range of the half-precision format.We develop an implementation with the CUDA platform, which, on most recent graphics processing units (GPU), is nearly twice as fast and uses half the memory of the equivalent single-precision version. The error on seismograms caused by the reduced precision is shown to correspond to a negligible fraction of the total seismic energy and is mostly incoherent with seismic phases. Finally, we find that this noise does not adversely impact full-waveform inversion nor reverse time migration, which both benefit from the higher throughput of half-precision computation.