We present models for the hydrodynamics of the impact of the envelope of SN 1987A with its inner circumstellar ring and for the resulting X-ray spectra and light curves. If the impact begins in A.D. 2000, the X-rays should be bright enough to resolve several emission lines with spectrometers on-board AXAF and Astro-E; if it begins in A.D. 2005, the X-rays will be roughly an order of magnitude brighter and have harder spectra. We compare our results with those from previous models and provide scaling laws to extend our results to models with impact times and ring densities different from those presented here. Within a few years after impact, the X-rays will brighten and their spectra will harden, owing to a complex variation of temperature within the shocked ring caused by the merger of primary and reflected shocks. The impact will continue for decades, and the X-rays will steadily increase in luminosity and temperature as the shock enters heretofore unseen matter in the ring.