We use a parallel spectral-element method to simulate the propagation of seismic waves generated by earthquakes in the entire 3-D Earth. The method is implemented using MPI on a large PC cluster (Beowulf) with 151 processors and 76 Gb of RAM. It is based upon a weak formulation of the equations of motion and combines the flexibility of a finite-element method with the accuracy of a pseudospectral method. The finite-element mesh honors all discontinuities in the Earth velocity model. To maintain a relatively constant number of grid points per seismic wavelength, the size of the elements is increased with depth in a conforming fashion, thus retaining a diagonal mass matrix. The effects of attenuation and anisotropy are incorporated. We benchmark spectral-element synthetic seismograms against a normalmode reference solution for a spherically symmetric Earth velocity model. The two methods are in excellent agreement for all waves with periods greater than 20 seconds.