<p>Steady shock wave shapes are studied in a size-dependent Cosserat continuum. The Cosserat continuum enriches a standard continuum by introducing a deformable triad of linearly independent director vectors that are determined by additional balances of director momentum, which introduce size-dependence. Limiting attention to purely mechanical nonlinear elastic response, it is shown that steady shock waves in uniaxial strain admit non-trivial trailing wave shapes after the jump at the shock front. The dependence of the wave shapes on the Cosserat material parameters are investigated for weak and strong shocks.</p>