Molecular dynamics simulations were carried out to investigate the mechanical properties of silicon nanoparticles during uniaxial compression by a flat-punch indenter. We considered a large set of systems, with dimensions in the range 10 nm to 50 nm, and various shapes like cubic (perfect and blunt), spherical, truncated spherical, and Wulff-shaped, as well as two compression orientations and two temperatures. Thorough analyses of the simulations first revealed that the relation between nanoparticle size and strength, usually termed as 'smaller is stronger', is critically dependent on the nanoparticle shape, at least for the investigated size range. For instance, a significant and size-dependent strength decrease is determined for facetted Wulff-like nanoparticles, but not for cubic or spherical systems for compression along <100>. We also found that the nanoparticle shape greatly influences plasticity. Several original plasticity mechanisms are obtained, among which the nucleation of half-loop V-shaped dislocation contained in two different {111} planes, dislocations gliding in unusual {110} planes, or the nucleation of partial dislocations in shuffle {111} planes. Our investigations suggest that plasticity properties are mainly governed by the localization of shear stress build up during elastic loading, and the geometry of surfaces in contact with indenters, these two characteristics being intimately related to the nanoparticle shape.