A spectral atlas of X-ray lines in the wavelength range 7.47-18.97 Å is presented, based on high-resolution spectra obtained during two M-class solar flares (on 1980 August 25 and 1985 July 2) with the Flat Crystal Spectrometer on board the Solar Maximum Mission. The physical properties of the flaring plasmas are derived as a function of time using strong, unblended lines. From these properties, predicted spectra using the CHIANTI database have been obtained, which were then compared with wavelengths and fluxes of lines in the observed spectra to establish line identifications. Identifications for nearly all the observed lines in the resulting atlas are given, with some significant corrections to previous analyses of these flare spectra. Line ratios allowed us to determine temperature and density; in the 1985 July 2 flare, very high densities (Ne~=1013 cm-3) were measured.