In this paper we report a theoretical study of Cepheid variables. Large grids, containing in total about 6 models, were calculated at varying mass, effective temperature, initial chemical composition, and mass-luminosity relation, the latter variable corresponding to different underlying evolutionary schemes for intermediate-mass stars, viz., classical models, models with mild core overshoot, and models with large core overshoot. The chemical abundances were chosen in order to bracket the abundances of the Cepheid stars in the Milky Way and in the Magellanic Clouds. The instability strips for three modes of pulsation (fundamental, first overtone, and second overtone) have been obtained, and analytical fits to the effective temperature and luminosity along the blue and red edges of the instability strips are presented. The theoretical data have been converted to magnitudes and colors of the UBVR(C)I(C) passbands, and the luminosity-period, luminosity-period-color, luminosity-period-color-mass relations have been derived. The results are presented in detail for the BV and VI passbands. Brief comparisons of the present results with the observational data for Cepheid variables allow us first to test the quality of the models and second to draw some conclusions. In particular, (1) the instability strip in the color-magnitude diagram widens as luminosity increases, and the predicted width of the Galactic instability strip in B - V is within 20% of that observed; (2) there is some indication that full-overshoot models are able to explain the properties of the Cepheid stars better than classical models, leading to an easy solution of the mass-discrepancy problem; and (3) we suggest that abundance-dependent studies of Cepheids that rely on B - V as a color should be treated with caution. It would be much better to use V - I as a color.
