The interaction of oblique monochromatic incident waves with a horizontal flexible membrane is investigated in the context of two-dimensional linear hydro-elastic theory. First, analytic diffraction and radiation solutions for a submerged impermeable horizontal membrane are obtained using an eigenfunction expansion method. Secondly, a multi-domain boundary element method (BEM) is developed to confirm the analytic solutions. The inner solution based on a discrete membrane dynamic model and simple-source distribution over the entire fluid boundaries is matched to the outer solution based on an eigenfunction expansion. The numerical solutions are in excellent agreement with the analytic solutions. The theoretical prediction was then compared to a series of experiments conducted in a two-dimensional wave tank at Texas A&M University. The measured reflection and transmission coefficients reasonably follow the trend of predicted values. Using the computer program developed, the performance of surface-mounted or submerged horizontal membrane wave barriers is tested with various system parameters and wave characteristics. It is found that the horizontal flexible membrane can be an effective wave barrier if properly designed.