Elastic wave propagation within and around the Los Angeles basin during the Whittier-Narrows earthquake in 1988 is simulated with a 3-D finite difference method. The model consists mainly of a sedimentary layer over the basement, but lateral variations inside the sedimentary basin is also included to approximate observed variations in surface shear velocity. The minimum shear velocity is 1 km/sec on the surface and fairly reliable results are obtained up to 0.75 Hz. The total simulation lasts 26 sec. Our simulation can reproduce the general amplification pattern: small east of the epicenter and large in the L.A. basin and the San Fernando Valley, due to thick sediments of low velocity in these areas. Surface waves are generated by the primary S wave and trapped inside the basins. In the southern part of the L.A. basin, a distinct later phase, delayed by 5 to 6 sec relative to the primary S wave, is produced in our simulation, which matches some strong motion records.