Tables 1 to 10 are only available in electronic form at CDS via anonymous ftp to cdsarc.u-strasbg.fr ( 130.79.128.5 ) or via http : //cdsweb.u-strasbg.fr/Abstract.html We present theoretical equivalent widths for the sum of the two strongest lines of the Calcium Triplet , CaT index , in the near-IR ( \lambda \lambda 8542 , 8662 Ã ) , using evolutionary synthesis techniques and the most recent models and observational data for this feature in individual stars . We compute the CaT index for Single Stellar Populations ( instantaneous burst , standard Salpeter-type IMF ) at four different metallicities , Z=0.004 , 0.008 , 0.02 ( solar ) and 0.05 , and ranging in age from very young bursts of star formation ( few Myr ) to old stellar populations , up to 17 Gyr , representative of galactic globular clusters , elliptical galaxies and bulges of spirals . The interpretation of the observed equivalent widths of CaT in different stellar systems is discussed . Composite-population models are also computed as a tool to interpret the CaT detections in star-forming regions , in order to disentangle between the component due to Red Supergiant stars , RSG , and the underlying , older , population . CaT is found to be an excellent metallicity-indicator for populations older than 1 Gyr , practically independent of the age . We discuss its application to remove the age-metallicity degeneracy , characteristic of all studies of galaxy evolution based on the usual integrated indices ( both broad band colors and narrow band indices ) . The application of the models computed here to the analysis of a sample of elliptical galaxies will be discussed in a forthcoming paper ( Gorgas et al . 1997 ) .