We present an extensive analysis of rare K decays, in particular of the two neutrino modes K+→pi+ nu nu-bar and KL→pi0 nu nu-bar, in the Minimal Supersymmetric extension of the Standard Model. We analyse the expectations for the branching ratios of these modes, both within the restrictive framework of the minimal flavour violation hypothesis and within a more general framework with new sources of flavour-symmetry breaking. In both scenarios, the information that can be extracted from precise measurements of the two neutrino modes turn out to be very useful in restricting the parameter space of the model, even after taking into account the possible information on the mass spectrum derived from high-energy colliders, and the constraints from B-physics experiments. In the presence of new sources of flavour-symmetry breaking, additional significant constraints on the model can be derived also from the two KL→pi0 l+l- modes.
