We observed the Seyfert 1 galaxy NGC 3516 twice during the flight of Astro-2 using the Hopkins Ultraviolet Telescope aboard the Space Shuttle Endeavour in March 1995. Simultaneous X-ray observations were performed with the Advanced Satellite for Cosmology and Astrophysics. Our far-ultraviolet spectra cover the spectral range 820-1840 Angstrom, with a resolution of 2-4 Angstrom. No significant variations were found between the two observations. The total spectrum shows a red continuum, f(nu) similar to nu(-1.89), with an observed flux of 2.2 x 10(-14) ergs cm(-2) s(-1) Angstrom(-1) at 1450 Angstrom, slightly above the historical mean. Intrinsic absorption in Ly beta is visible as well as absorption from O VI lambda lambda 1032, 1038, N V lambda lambda 1239, 1243, Si IV lambda lambda 1394, 1403, and C IV lambda lambda 1548, 1551. The UV absorption lines are far weaker than is usual for NGC 3516 and also lie closer to the emission-line redshift rather than showing the blueshift typical of these lines when they are strong. The neutral hydrogen absorption, however, is blueshifted by 400 km s(-1) relative to the systemic velocity, and it is opaque at the Lyman limit. The sharpness of the cutoff indicates a low effective Doppler parameter, b < 20 km s(-1). For b = 10 km s(-1), the derived intrinsic column density is 3.5 x 10(17) cm(-2). As in NGC 4151, a single warm absorber cannot produce the strong absorption visible over the wide range of observed ionization states. Matching both the UV and X-ray absorption simultaneously requires absorbers spanning a range of 10(3) in both ionization parameter and column density.