Sensitivity analysis and uncertainty estimation are crucial to the validation and calibration of numerical models. In this paper we present the application of sensitivity analyses, parameter estimations and Monte-Carlo uncertainty analyses on TEPHRA, an advection-diffusion model for the description of particle dispersion and sedimentation from volcanic plumes. The model and the related sensitivity analysis are tested on two sub-plinian eruptions: the 22 July 1998 eruption of Etna volcano (Italy) and the 17 June 1996 eruption of Ruapehu volcano (New Zealand). Sensitivity analyses are key to (1) constrain crucial eruption parameters (e.g., total erupted mass) (2) reduce the number of variables by eliminating non-influential parameters (e.g., particle density) and (3) investigate the interactions among all input parameters (plume height, total grain-size distribution, diffusion coefficient, fall-time threshold and mass-distribution parameter). For the two test cases, we found that the total erupted mass significantly affects the model outputs and, therefore, it can be accurately estimated from field data of the fallout deposit, whereas the particle density can be fixed at its nominal value because it has negligible effects on the model predictions.