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The increased complexity of contemporary constitutive models for soils requires a rigorous method to evaluate the effect of the large number of model parameters on the results. Ideally, the interaction effects between the individual parameters should also be quantified. This is achieved by combining a state-of-the-art global sensitivity method with a general purpose Finite Element Method (FEM) for geotechnics. The method is tested for the non-trivial example of coupled hydro-mechanical response of clay in oedometric compression. The results indicate that proposed method for rigorous sensitivity analysis provides a feasible, yet more powerful, alternative to the method commonly used by engineers, i.e. the sequences of one-factor-at-a-time (OFAT) trails.