Taking account of uncertainties in models is crucial to improving robustness. The greater the complexity of the systems to be studied, the more variabilities may arise. In particular, uncertainties arising from non-linearities in dynamics and from the multi-physics of certain phenomena are dealt with here. The variabilities are modelled by introducing uncertainties in the parameters using various methods, in particular the Monte Carlo method, polynomial chaos development and the non-intrusive probabilistic collocation method. The impact generated on output quantities shows a probabilistic range of system operation. In rotor vibration, many parameters create strong variations in the vibratory response, whether they are associated with the mode of use (operator, experimental - FUI Sicodyn) or the system itself and its environment (material, geometry, excitation, boundary conditions). It is sometimes necessary to identify certain parameters. Predicting the behaviour of existing multiphysical systems or systems under design is becoming essential. In addition, some materials require a multi-scale design for optimum performance. The variability associated with multiphysics coupling and macroscopic performance is not negligible. Initial studies show these influences (MURMUR project) on an example of chemico-bio-mechanical multiphysical coupling. Research is underway on a multi-scale thermo-mechanical problem with damage.