A laser-based ultrasonic technique using a pulsed laser for stimulating ultrasonic waves in fiber-reinforced composite materials is the subject of investigation. For convenience, the material is chosen to be homogeneous transversely isotropic. The study is strictly limited to the laser power regimes that are suitable for nondestructive evaluation. An elastodynamic methodology is presented based on integral formulation in order to develop a representation for the dynamic responses in terms of the characteristics of the source that originated the motion. This requires a computation of elastodynamic Green function which represents the displacement field from the idealized synthetic sources localized precisely in both space and time. A two-dimensional numerical analysis utilizing a finite difference method for computation of the Green function in a finite plate is developed which provides the basis for quantitative nondestructive evaluation of fiber reinforced composite materials. Numerical results are presented for the surface displacement at the epicenter. Prediction based on numerical simulations are compared with experimental results.