We consider a geometric inverse problem of recovering some material parameters of an unknown elastic body by probing with elastic waves that scatter once inside the body. That is we send elastic waves from the boundary of an open bounded domain. The waves propagate inside the domain and scatter from an unknown point scatterer. We measure the entering and exiting directions of the waves and their total travel times. Geometrically this is equivalent to knowing the broken scattering relation of the unknown wave speed. The broken scattering relation consists of the total lengths of broken geodesics that start from the boundary, change direction once inside the manifold, and propagate to the boundary. We show that if two reversible Finsler manifolds satisfying a convex foliation condition have the same broken scattering relation, then they are isometric. The talk is based on a joint work with: M.V. de Hoop, J. Ilmavirta and M. Lassas