Abstract: After giving quick overviews of critical collapse and a formalism of relativistic elasticity, I will discuss recent work aimed at analyzing critical collapse with elastic materials. It is well-known that gravitational collapse in (non-elastic) perfect fluid models displays emergent continuous self-similarity at the threshold of black hole formation. Such matter models can be extended to include relativistic elasticity effects, and continuous self-similar configurations arise in this context when choosing a scale-invariant elastic matter model. A discrete family of such threshold solutions is determined numerically by solving an associated boundary value problem. I will present various results for these modes and discuss how their properties are affected by elasticity parameters, namely the shear index and the Poisson ratio.