We present a new evolutionary stellar population synthesis model, which predicts spectral energy distributions for single-age single-metallicity stellar populations (SSPs) at resolution 1.5 Å (FWHM) in the spectral region of the near-infrared CaII triplet feature. The main ingredient of the model is a new extensive empirical stellar spectral library that has been recently presented by Cenarro et al., which is composed of more than 600 stars with an unprecedented coverage of the stellar atmospheric parameters. Two main products of interest for stellar population analysis are presented. The first is a spectral library for SSPs with metallicities -1.7 < [Fe/H] < +0.2, a large range of ages (0.1-18 Gyr) and initial mass function (IMF) types. They are well suited to modelling galaxy data, since the SSP spectra, with flux-calibrated response curves, can be smoothed to the resolution of the observational data, taking into account the internal velocity dispersion of the galaxy, allowing the user to analyse the observed spectrum in its own system. We also produce integrated absorption-line indices (namely CaT*, CaT and PaT) for the same SSPs in the form of equivalent widths. We find the following behaviour for the CaII triplet feature in old-aged SSPs: (i) the strength of the CaT* index does not change much with time for all metallicities for ages larger than ~3 Gyr; (ii) this index shows a strong dependence on metallicity for values below [M/H]~-0.5 and (iii) for larger metallicities this feature does not show a significant dependence either on age or on the metallicity, being more sensitive to changes in the slope of power-like IMF shapes. The SSP spectra have been calibrated with measurements for globular clusters by Armandroff & Zinn, which are well reproduced, probing the validity of using the integrated CaII triplet feature for determining the metallicities of these systems. Fitting the models to two early-type galaxies of different luminosities (NGC 4478 and 4365), we find that the CaII triplet measurements cannot be fitted unless a very dwarf-dominated IMF is imposed, or if the Ca abundance is even lower than the Fe abundance. More details can be found in work by Cenarro et al.