We generated, for the first time, a very comprehensive set of estimates of cross-section covariance data in the neutron energy range of 5 keV to 20 MeV. The covariance matrices were obtained for 307 materials, from 19F to 209Bi, covering structural materials, fission products, and heavy nonfissile nuclei. These results offer model-based, consistent assessments of covariance data for nuclear criticality safety applications. The evaluation methodology combines the nuclear reaction model code EMPIRE, which calculates the sensitivity of the cross sections to nuclear reaction model parameters, and the Bayesian code KALMAN, which propagates uncertainties of the model parameters to these cross sections. Taking into account the large number of materials studied, we refer only marginally to experimental data. The covariances were derived from the perturbation of several key model parameters selected by the sensitivity analysis. These parameters refer to the optical model potential, the level densities, and the strength of the preequilibrium emission. Our work represents the first attempt to generate neutron cross-section covariances on such a large scale.