Major developments, especially in the aircraft, automobile and energy sectors, have led to the need to use highly featured new materials used in these fields. Carbon fiber reinforced plastics (CFRP) have been used frequently in the transportation and energy sectors because of their high strength-to-weight ratio. Mathematical Modeling of laser beam ablation of carbon fiber reinforced plastic (CFRP) is performed. Heat transfer equation based on Fourier's law of conduction is used for calculation of the temperature distribution in the target material. Under some natural regularity and consistency conditions on the input data the existence, uniqueness of solution are shown by using the generalized Fourier method.