Let G be a domain in ℝ^m with compact closure G¯, m ≥ 2. The boundary ∂G may contain nonintersecting closed smooth “edges” of various dimensions. In the cylinder {(x, t) : x ∈ G, −∞ < t < +∞}, we study the equations of elastodynamics. The Dirichlet condition (displacements) or the Neumann condition (stresses) is given on the boundary ∂G× ℝ of the cylinder. The goal is to describe the behavior of solutions near edges.