This paper develops a system with quasi-particles on a discrete lattice, Hamiltonian description of this system is presented,which can simulate acoustic and elastic waves. The nine-point interaction models are used and interaction coefficients are determined in this system. The connection between Hamiltonian system approach and acoustic or elastic wave equations are proved, and the relations between their physical quantities are presented. The symplectic algorithms that are used in the given media models and simulation results are presented.