In this paper, guided elastic Lamb wave propagation characteristics in laminated plates are studied using a proper phenomological model for the fiber reinforced composite material. It is well established that ultrasonic waves attenuate in FRP composite material. This is caused by the visco-elastic behavior of the resin ad scattering due to the fiber. The material here is, therefore, numerically modeled using complex material properties. Both the material and frequency-dependent damping for each layer of the laminated plate is incorporated in the formulation. A Rayleigh-Ritz based stiffness method is used to discretize the plate in the vertical direction to determine wave numbers. Furthermore, elasto-dynamic Green functions for both displacement and stress fields in the laminated composite plate are also derived. In this manner, the effect of guided wave attenuation on wave numbers and displacements and stress Green functions are studied. All wave numbers, including those for propagating modes, are complex. However, the relative value of the imaginary part of the wave number of the propagating modes are small, and it is seen that incorporation of damping has an insignificant effect on dispersion characteristics, irrespective of the excitation frequency. However, it significantly affects both displacement and stress fields, especially as the distance from the source increases. This effect is dependent on the excitation frequency. At relative low frequencies, the attenuation of the displacement and stress fields is small. The attenuation increases with excitation frequency, although seemingly the effects on the stress field are relatively less significant than those on the displacement field.