This research explores elastodynamics and wave propagation in fractal micropolar solid media. Such media incorporate a fractal geometry while being modelled constitutively by the Cosserat elasticity. The formulation of the balance laws which govern the mechanics of fractal micropolar solid media is presented. Four eigenvalue-type elastodynamic problems admitting closed-form analytical solutions are introduced and discussed. A numerical procedure to solve general initial boundary value wave propagation problems in three-dimensional micropolar bodies exhibiting geometric fractality is then applied. Verification of the numerical procedure is discussed using the analytical solutions.