The increasing knowledge and understanding of volcanic sources has led to the development and implementation of sophisticated and complex mathematical models with the main goal of describing field and experimental data. Quantification of the model's ability in describing the data becomes fundamental for a realistic estimate of the model parameters. The analysis of sensitivity can help us in identifying the parameters that significantly affect the model's output and in assessing its quality factor. In this paper, we describe the Global Sensitivity Analysis (GSA) methods based both on Fourier Amplitude Sensitivity Test and on the Sobol' approach and discuss their implementation in a Matlab software tool (GSAT). We also introduce a new criterion for model selection based on sensitivity analysis. The proposed approach is tested and applied to quantify the fitting ability of an analytic volcanic source model on a synthetic deformation data. Results show the validity of the method, against the traditional approaches, in supporting the volcanic model selection and the flexibility of the GSAT software tool in analyzing the model sensitivity.