Composite materials are used in many advanced engineering applications because of their high specific strength and specific stiffness. However, the complex damage mechanisms and failure modes are still not well-understood and limit their wide-spread applications. It is critical to monitor the structural heath for improved understanding of damage evolution and accurate life estimation. Ultrasonic wave based structure health monitoring (SHM) technique is a promising approach and has been investigated by many researchers. However, for the techniques to be reliable, it is necessary to understand the wave propagation behavior in composites. A fully coupled numerical simulation model has been developed to understand wave propagation and dissipation in composites under different excitation frequencies. The model is based on the local interaction simulation approaches/sharp interface model (LISA/SIM), and is computationally efficient compared to traditional finite element methods. This model is used to emulate wave behavior in composites in the current work. The output sensor signals are processed using matching pursuit decomposition algorithm to study the zero-order anti-symmetric and symmetric Lamb wave modes, including attenuation effects and dispersion. The results show good agreement with published experiments. Sensitivity studies show that wave velocities and amplitudes vary significantly with changes in the material properties and stiffness.