In this paper, the problem involving Inviscid Flow with a free surface over an undulating bottom is studied within the framework of linear theory. Applying perturbation analysis in conjunction with the Fourier transform technique, the boundary value problem arising from the Flow problem is solved analytically. Behaviour of both interface and free-surface profiles, which are unknown at the outset, are analyzed. It is found that each profile (interface and free-surface) possesses a wave free region at the far upstream, followed by a modulated downstream wave. It also observed, for the first time, that the amplitude of the downstream wave is varying. Further, the effects of various system parameters are analyzed and demonstrated in graphical forms.