We have developed a new stellar population synthesis model designed to study early-type galaxies. It provides optical and near-infrared colors, and line indices for 25 absorption lines. It can synthesize single age, single metallicity stellar populations, or follow the galaxy through its evolution from an initial gas cloud to the present time. The model incorporates the new isochrones of the Padova group and the latest stellar spectral libraries. We have applied our model to new data for a set of three early-type galaxies to find out whether these can be fitted using single-age old metal-rich stellar populations, as is normal practice when one uses other stellar models of this kind. The model is extensively compared with previous ones in the literature to establish its accuracy as well as the accuracy of this kind of models in general. Using the evolutionary version of the model we find that we cannot fit the most metal-rich elliptical galaxies if we keep the IMF constant and do not allow infall of gas. We do, however, reproduce the results of Arimoto & Yoshii for the evolution of the gas, and produce colors, and, for the first time with this type of models, absorption line strengths. It is in fact possible to fit the data for the elliptical galaxies by varying the IMF with time. Our numerical model is in good broad agreement with the analytical simple model. We prefer, however, to calculate the evolution of the gas numerically instead of using the simple model, since it offers more flexibility, and even improved insight, when comparing with observations. In the present paper we describe the model, and compare a few key observables with new data for three early-type standard galaxies. However, the data, as well as our fits, will be discussed in much more detail in a second paper (by Vazdekis et al.), where some conclusions will be drawn about elliptical galaxies on the basis of this model.