AbstractMost of the physical processes driving the TP-AGB evolution are not yet fully understood and they need to be modelled with parameterised descriptions. We present the results of the on-going calibration of the TP-AGB phase based on a complete sample of AGB stars in the Small Magellanic Cloud (SAGE-SMC survey). We computed large grids of TP-AGB models with several combinations of third dredge-up and mass-loss prescriptions with the COLIBRI code. The SMC AGB population is modelled with the population synthesis code TRILEGAL according to the space-resolved star formation history derived with the deep photometry from the VISTA survey of the Magellanic Clouds. We put quantitative constraints on the efficiencies of the third dredge-up and mass loss by requiring the models to reproduce the star counts and the luminosity functions of the observed Oxygen-, Carbon-rich and extreme-AGB stars and we investigate the impact of the best-fitting prescriptions on the chemical yields.