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Lattice Boltzmann methods (LBM) have become a well-established tool in fluid dynamics due to their simplicity, efficiency, and ability to handle complex geometries. In recent years, interest has grown in extending LBM to solid mechanics in order to exploit the same advantages. This work presents SolidLBM, a framework for elastodynamics based on the moment-chain approach. The method targets the solution of the balance laws for linear elastic materials and is presented in a modular fashion. This provides an in-depth account of the framework, including implementation details. The algorithms follow the same philosophy, provided as an open-source Python package that serves as the reference implementation of the framework. The behaviour of the method is first analysed with the BGK collision operator, followed by a systematic investigation of stability. This leads to the introduction of a two-relaxation-time (TRT) scheme. An optimisation-based parameter study provides guidance for the choice of relaxation parameters. Benchmark problems demonstrate the viability of the approach, with validation against finite element simulations and an investigation into the convergence behaviour. Examples of wave propagation in rods and beams are provided, showcasing the method’s ability to capture complex wave phenomena. The aspect of dissipation is regarded as an important factor in the simulation process. A comparative performance analysis highlights the computational efficiency of the method. The results establish SolidLBM as a capable and efficient approach for simulating elastodynamics. This work thoroughly discusses the capabilities and limitations of the proposed method. Avenues for future research and potential improvements are outlined, paving the way for further advancements in the field of lattice Boltzmann methods for solids. Beyond elastodynamics, the framework is extended to fracture mechanics. A dynamic lattice update algorithm is developed to simulate crack propagation, with a fracture criterion derived from configurational forces. The assessment of the fracture algorithm is conducted via a series of numerical tests, demonstrating its effectiveness in capturing crack propagation. The results indicate that the proposed method is capable of simulating fracture processes in brittle materials. This opens up new possibilities for using lattice Boltzmann methods in the study of fracture mechanics. Limitations in the approach and the coupling to the LBM are discussed, highlighting the need for further research in this area. The results underline both the opportunities of LBM in solid and fracture mechanics, and the challenges that remain, providing a clear basis and direction for future developments.