We present a non-LTE model atmosphere analysis of the B star secondary of ζ Aurigae (B5 V+K4 Ib) and determine its stellar parameters. A grid of model atmospheres and synthetic spectra were computed for stellar parameters typical of mid-B stars, using the TLUSTY and SYNSPEC codes of Hubeny with the lines and continua of H and He calculated in non-LTE. We observed ζ Aur with the Goddard High Resolution Spectrograph (GHRS) of the Hubble Space Telescope (HST) at several epochs near the 1993 eclipse. By carefully removing the circumstellar wind features at the two epochs furthest from eclipse, we recovered the intrinsic photospheric spectrum of the B star. The photospheric spectrum of ζAur B is compared to the grid of synthetic spectra, and the best fit is determined using a least-squares technique. We find T<SUB>eff</SUB> = 15,400±300 K, log g = 3.9±0.1, and V sin i = 200±15 km s<SUP>-1</SUP> The corresponding spectral type, using the effective temperature scale of Underhill et al., is B5 V. <P />The C I UV 5, 6, 7, and 9 resonance multiplets (1277-1281 Å) and the Si II UV 4 (1260-1265 Å) and UV 5 (1190-1197 A) resonance multiplets are observed to be much weaker than our models predict. We empirically determine departure coefficients of C I and Si II by varying the oscillator strengths of transitions of each of these ions until a good match with the GHRS spectra is obtained. For C I, we provide theoretical confirmation of these empirically determined departure coefficients by computing a more detailed model atmosphere including levels and transitions of C I, C II, and C III treated in non-LTE. The synthetic spectra computed from this model are in good agreement with the GHRS observations, and the C I ground-state departure coefficient is consistent with the empirically determined value. <P />We examine several possible causes of the weakness of the Si II lines and conclude that an underabundance due to non-LTE effects is the probable explanation. Previous model atmospheres including Si II computed in non-LTE show that the Si II resonance lines are formed essentially in LTE. We suggest that autoionization of Si II (neglected in previous modeling) may shift the silicon ionization balance enough to account for the weakness of the Si II lines.