The term 'solid-state turbulence' may sound like an oxymoron, but in fact it is not. In this article, we demonstrate that 'solid-state turbulence' may emerge owing to a defining property of the solid state: the ability of a solid to retain its shape. We consider shear flow under high-pressure torsion of layers of solids with different flow stress and show that the stiffer ones may spontaneously decompose into a set of blocks. This effect is fundamental for the occurrence of 'solid-state turbulence' (SST). To visualize SST, we use a heuristic model based on discretization of a continuum into interacting 'particles'. The outcomes of the numerical experiments conducted support the occurrence of pulsations of velocity and pressure in plastically deforming solids and the emergence of vortices characteristic of classical turbulence. This phenomenon may have important practical implications for solid-state mixing as an ecologically beneficial alternative to conventional metallurgical processing routes.