Monte Carlo calculations have been performed using MCNP code to study the optimization of photo-neutron yield for different electron beam energies impinging on Pb, W and Ta cylindrical targets of varying thickness. It is noticed that photo-neutron yield can be increased for electron beam energies $\geq 100$ MeV for appropriate thickness of the target. It is also noticed that it can be maximized by further increasing the thickness of the target. Further, at higher electron beam energy heat gradient in the target decreases, which facilitates easier heat removal from the target. This can help in developing a photo-neutron source based on electron LINAC by choosing appropriate electron beam energy and target thickness to optimize the neutron flux for ADS, transmutation studies and as high energy neutron source etc. Photo-neutron yield for different targets, optimum target thickness and photo-neutron energy spectrum and heat deposition by electron beam for different incident energy is presented.