In recent years, Lattice Boltzmann methods (LBMs) have been adapted to the simulation of elastodynamics. While LBMs are already quite versatile, this expands their usage well beyond the initial domain of kinetic theory. The resulting methods offer improved numerical performance when compared to the more established methods in computational solid mechanics. Such an LBM has been proposed for linear elastic materials [1] with appropriate handling [2] of Dirichlet– and Neumann–boundary conditions. Its definition follows that of fluid mechanics rather closely. However, the material modeling is more intricate, since stresses and strains have to be treated. Moreover, this method regards compressibility and highly dynamical phenomena. This gives rise to stability issues, which need to be examined. Nonetheless, this method has been used in the simulation of dynamic crack propagation [3]. This talk delivers an overview of this LBM for solids. Some details of material modelling and its incorporation into the LBM are described. The difficulties that arise, both systematic and numerical, are discussed and novel ideas to remedy these issues are introduced. Examples and applications of the method are showcased in this talk. [1] M. Escande, P. K. Kolluru, L. M. Cléon, and P. Sagaut, Lattice Boltzmann method for wave propagation in elastic solids with a regular lattice: Theoretical analysis and validation, Sep. 10, 2020. doi: 10.48550/arXiv.2009.06404. [2] E. Faust, A. Schlüter, H. Müller, F. Steinmetz, and R. Müller, “Dirichlet and Neumann boundary conditions in a lattice Boltzmann method for elastodynamics,” Com- putational Mechanics, Jul. 26, 2023, issn: 1432-0924. doi: 10.1007/s00466-023- 02369-w. [3] H. Müller, A. Schlüter, E. Faust, and R. Müller, “On dynamic crack propagation in a lattice Boltzmann method for elastodynamics in 2d,” PAMM, vol. 23, no. 3, e202300230, Sep. 19, 2023, issn: 1617-7061. doi: 10.1002/pamm.202300230.