Patient-specific cardiac modelling can help in understanding pathophysiology and predict therapy planning. However, it requires to personalize the model geometry, kinematics, electrophysiology and mechanics. Calibration aims at providing proper initial values of parameters before performing the personalization stage which involves solving an inverse problem. We propose a fast automatic calibration method of the mechanical parameters of a complete electromechanical model of the heart based on a sensitivity analysis and the Unscented Transform algorithm. A new implementation of the complete Bestel-Clement-Sorine (BCS) cardiac model is also proposed, in a modular and efficient framework. A complete sensitivity analysis is performed that reveals which observations on the volume evolution are significant to characterize the global behaviour of the myocardium. We show that the calibration method gives satisfying results by optimizing up to 5 parameters of the BCS model in only one iteration. This method was evaluated synthetically as well as on 7 volunteers with a mean relative error from the real data of 10 %. This calibration is designed to replace manual parameter estimation as well as initialization steps that precede automatic personalization algorithms based on images.