  Homogeneous multi-wavelength observations of classical Cepheids from the
forthcoming Rubin-LSST have the potential to significantly contribute to our
understanding of the evolutionary and pulsation properties of these pulsating
stars. Updated pulsation models for Classical Cepheid stars have been computed
under various assumptions about chemical compositions, including relatively low
metallicity ($Z$ = $0.004$ with $Y$ =$0.25$ and $Z$=$0.008$ with $Y$ =$0.25$),
solar metallicity ($Z$=$0.02$ with $Y$=$0.28$), and supersolar metallicity
environments ($Z$ = $0.03$ with $Y$ = $0.28$).
  From the predicted periods, intensity-weighted mean magnitudes, and colors,
we have derived the first theoretical pulsation relations in the Rubin-LSST
filters (ugrizy), including period-luminosity-color, period-Wesenheit, and
period-age-color relations. We find that the coefficients of these relations
are almost insensitive to the efficiency of superadiabatic convection but are
significantly affected by the assumption of the mass-luminosity relation and
the adopted chemical composition. Metal-dependent versions of these relations
are also derived, representing valuable tools for individual distance
determinations and correction for metallicity effects on the cosmic distance
scale.
