Although the literature on mechanical properties of nanostructures is extensive, there are still few studies focusing on core-shell nanoparticles. In these systems, which are interesting in a broad range of applications, one could genuinely assume that the softest part, be it the core or the shell, will first yield when submitted to compression. To test this view, we have carried out large scale molecular dynamics simulations of uniaxially compressed core-shell Si-SiC nanoparticles. Our first conclusion is that for the investigated size range (diameters equal or below 50 nm), the nanoparticles yield plastically with no signs of fracture, in agreement with experiments on single material systems. Furthermore, our investigations also reveal that depending on the shell thickness, plastic deformation is confined either in the core or in the shell. We propose a model, based on the theory of contact mechanics and geometrical arguments, to explain this surprising result. Furthermore, we find that for a specific shell to diameter ratio, corresponding to the transition between core and shell, the stress concentration in the nanoparticles is apparently hindered, leading to a delayed plastic deformation.