The narrow emission lines from the inner ring around SN 1987A during the first $\sim 2000$ days are modeled. The analysis extends that in Lundqvist & Fransson (1991) to include an improved description for the geometry, a multi-density structure of the emitting gas, results from improved calculations for the evolu- tion of the EUV radiation from the outburst, and updated atomic data. The ring has to be optically thick to the ionizing radiation, as is the case for a ring geometry, but not for a spherical shell. The density of the observed gas in the ring ranges from $(6.0\pm1.0)\EE{3} \cm3$ to $3.3\EE{4} \cm3$. The early ($t \lesssim 410$ days) UV line emission is dominated by the gas with the high- est density. Gas of lower density than $\sim 6\EE{3} \cm3$ may be present in the ring, but will not dominate the emission until after $\sim 2000$ days. The ionized mass observed up to day 1882 is $\sim 4.5\EE{-2} \Msun$. The He/H ratio is $0.25\pm0.05$, and the overall abundance of C, N and O is $0.30\pm0.05$ times solar with relative abundances ${\rm N/C} = 5.0\pm2.0$ and ${\rm N/O} = 1.1\pm0. 4$. The peak effective temperature of the burst is in the range $(5-8)\EE{5}$ K. The corresponding color temperature is $(1.0-1.5)\EE6$ K. To model the $\NV$~ $λ$1240 light curve, resonance scattering in a medium external to the ring is needed. It is shown that the $\NV$ line scattering can be used to discrimi- nate between models for the formation of the inner ring and the extended nebula.

38 pages PostScript, 7 PostScript figures may be retrieved from ftp://www.astro.su.se/pub/supernova/lf95_87A/ Accepted for publication in ApJ