Bio-mechanical breast simulations are based on a gravity free geometry as a reference domain and a nonlinear mechanical model parameterised by physical coefficients. As opposed to complex models proposed in the literature based on medical imagery, we propose a simple but yet realistic model that uses a basic set of measurements easy to realise in the context of routinely operations. Both the mechanical system and the geometry are controlled with parameters we shall identify in an optimisation procedure. We give a detailed presentation of the model together with the optimisation method and the associated discretisation. Sensitivity analysis is then carried out to evaluate the robustness of the method.