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{AA}), 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 17Gyr, 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).