The dynamic behavior of mono-and nanocrystalline SiC ceramics under plane shock loading is revealed using molecular-dynamics simulations. The generation of shock-induced elastic compression, plastic deformation, and structural phase transformation is characterized at different crystallographic directions as well as on a 5-nm grain size nanostructure at 10 K and 300 K. Shock profiles are calculated in a wide range of particle velocities 0.1-6.0 km/s. The predicted Hugoniot agree well with experimental data. Results indicate the generation of elastic waves for particle velocities below 0.8-1.9 km/s, depending on the crystallographic direction. In the intermediate range of particle velocities between 2 and 5 km/s, the shock wave splits into an elastic precursor and a zinc blende-to-rock salt structural transformation wave, which is triggered by shock pressure over the $90 GPa threshold value. A plastic wave, with a strong deformation twinning component, is generated ahead of the transformation wave for shocks in the velocity range between 1.5 and 3 km/s. For particle velocities greater than 5-6 km/s, a single overdriven transformation wave is generated. Surprisingly, shocks on the nanocrystalline sample reveal the absence of wave splitting, and elastic, plastic, and transformation wave components are seamlessly connected as the shock strength is continuously increased. The calculated strengths 15.2, 31.4, and 30.9 GPa for h001i, h111i, and h110i directions and 12.3 GPa for the nanocrystalline sample at the Hugoniot elastic limit are in excellent agreement with experimental data.