<p>The lattice Boltzmann method (LBM) has been successfully applied to the simulation of fluid flows for over three decades. In recent years, it has also been extended to solid mechanics, particularly for elastodynamics. This work presents a comprehensive introduction to the moment chain LBM for solids, focusing on the two-relaxation-time (TRT) scheme. The method is based on a chain of balance equations, which allows for the simulation of wave propagation in elastic solids. The TRT scheme improves stability and accuracy, making it suitable for a wide range of material parameters. The method is applied to wave propagation in solids with an analysis of the energy dissipation. The results demonstrate the effectiveness of the moment chain LBM for simulating elastodynamics and highlight its potential for future applications in solid mechanics.</p>