In recent years, Lattice Boltzmann methods (LBM) have attracted increasing interest for applications in solid mechanics. We have developed a modular LBM framework for lastodynamics [1,2], based on a moment chain that consistently reproduces the balance equations. Material behaviour is incorporated through constitutive source terms, which have been extended to stress–strain relations of nonlinear elasticity [3]. In this presentation, we introduce the framework and discuss key modelling aspects, including the choice of collision operator, the formulation of source terms for material modelling, and influences on energy dissipation. We further clarify how the numerical model is connected to the underlying physical principles. The characteristics of the proposed LBM are investigated using benchmark problems and wave propagation simulations, demonstrating its suitability for dynamic systems. In addition, we explore applications in fracture mechanics, with a focus on the simulation of crack growth [4]. [1] E. Faust et al. “Dirichlet and Neumann boundary conditions in a lattice Boltzmann method for elastodynamics”. In: Computational Mechanics 73.2 (2024). doi: 10.1007/00466-023-02369-w. [2] H. Müller and R. Müller. “Two-relaxation-time lattice Boltzmann method for elastodynamic wave propagation in solids”. In: Computational Particle Mechanics (2025). doi: 10.1007/s40571-025-01065-1. [3] H. Müller, E. Faust, A. Schlüter, and R. Müller. “Extending the Lattice Boltzmann Method to non-linear elastodynamics”. In: Computer Methods in Applied Mechanics and Engineering 443 (2025). doi: 10.1016/j.cma.2025.118076. [4] H. Müller, A. Schlüter, E. Faust, and R. Müller. “On dynamic crack propagation in a lattice Boltzmann method for elastodynamics in 2D”. In: PAMM 23.3 (2023). doi: 10.1002/pamm.202300230.