We present a basic model for the calculation of the luminosity distribution of supernova remnant populations. We construct theoretical H$\rm \alpha \,$and joint [S ii] - H$\rm \alpha \,$luminosity functions for supernova remnants by combining prescriptions from a basic evolution model that provides the shock velocity and radius for SNRs of different age and pre-shock density, with shock excitation models that give the gas emissivity for shocks of different physical parameters. We assume a flat age distribution, and we explore the effect of different pre-shock density distributions or different magnetic parameters. We find very good agreement between the shape of the model H$\rm \alpha \,$and the joint [S ii] - H$\rm \alpha \,$luminosity functions and those measured from SNR surveys in nearby galaxies.