In this paper, the non-Fourier effect in a slab subjected to a periodic thermal disturbance is investigated by deriving the analytical solution of the hyperbolic heat conduction equation. The temperature profiles at the front and rear surfaces of the slab are calculated for various relaxation time. By comparing the results with those obtained from the Fourier parabolic heat conduction equation, a transition condition between the ’parabolic’ and ’hyperbolic’ behavior at both surfaces is obtained. The phase and amplitude difference between the front and the rear surface is calculated numerically as a function of the relaxation Fourier number and the results are shown graphically.