Acoustic emission (AE) occurring in concrete fracture process is a combination of concrete fracture at local material level and the propagation of induced elastic waves at structural level. Simulation of the fracture-induced AE in concrete needs a model that is able to address the fracture behavior and the wave propagation at the same time. However, to date, no available modelling tools can simulate the whole fracture-induced AE process. Among others, the lattice models have the potential to achieve the simulation of the whole fracture-induced AE process. However, the lattice models are currently restricted to statistical analysis of AE events in fracture process. This paper investigates the feasibility and limitation of lattice model for the simulation of elastic wave propagation process. Several simulation cases are performed considering the propagation of both plane waves and point-source waves. The simulation results, in terms of wave velocity and geometric spreading loss of wave amplitudes, agree well with the analytical solutions. This study represents the first step for the simulation of complete fracture-induced AE waves in concrete.