Ageing and newly built critical engineering structures require monitoring for potential material defects and structural damage. Guided ultrasonic waves have been widely used in many structural damage detection applications for decades. Recent years have shown more research interest in nonlinear propagation of such waves. The paper investigates nonlinear shear horizontal waves. Research interest in this area is driven by advancements in technological capabilities for excitation and relatively good sensitivity to micro-structural defects. The latter mainly refers to the higher harmonic generation. The major focus of the work undertaken is on the fundamental mode due to its non-dispersive nature. Since distinguishing between global material-related and local defect-related nonlinearities is still problematic more simulation work is needed in this area of research. Nonlinear crack-wave interaction is investigated. Local crack-induced nonlinear elasticity and dissipation are modelled using hysteresis. Numerical simulations of crack-wave interaction are performed using the Local Interaction Simulation Approach, allowing not only for top-down solution of nonlinear differential equations but also for parallel computing architecture. Modelling and numerical simulations are undertaken to reveal various nonlinear phenomena. This includes not only higher harmonic generation but also nonlinear vibro-acoustic modulations. Numerical simulations demonstrate that cracks can be effectively represented using localised models of hysteresis that have been previously used for modelling of distributed material nonlinearity. The study show that the level of nonlinearity depends not only on the excitation amplitude but also on the modeled area that covers the crack and its vicinity. The latter refers to the plastic zone of the crack.