We present a new library of fully-radiative shock models calculated with the MAPPINGS III shock and photoionization code. The library consists of grids of models with shock velocities in the range v=100-1000 km/s and magnetic parameters B/sqrt(n) of
10^-4 - 10 muG cm^(3/2) for five different atomic abundance sets, and for a pre-shock density of 1.0 cm^(-3). Additionally, Solar abundance model grids have been calculated for densities of 0.01, 0.1, 10, 100, and 1000 cm^(-3) with the same range in v and B/sqrt(n). Each model includes components of both the radiative shock and its photoionized precursor, ionized by the EUV and soft X-ray radiation generated in the radiative gas. We present the details of the ionization structure, the column densities, and the luminosities of the shock and its precursor. Emission line ratio predictions are separately given for the shock and its precursor as well as for the composite shock+precursor structure to facilitate comparison with observations in cases where the shock and its precursor are not resolved. Emission line ratio grids for shock and shock+precursor are presented on standard line ratio diagnostic diagrams, and we compare these grids to observations of radio galaxies and a sample of AGN and star forming galaxies from the Sloan Digital Sky Survey. This library is available online, along with a suite of tools to enable the analysis of the shocks and the easy creation of emission line ratio diagnostic diagrams. These models represent a significant increase in parameter space coverage over previously available models, and therefore provide a unique tool in the diagnosis of emission by shocks.
