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We present the numerical study of scattering of scalar waves from impenetra­ble two-dimensional periodic surfaces of arbitrary shape. Nearly all numerical simulations of scattering of waves from rough surfaces in the past have been limited to one-dimensional surfaces and moderate angles of incidence. By making the surface infinite and bi-periodic, it becomes possible to simulate numerically scattering from two-dimensional surfaces, even down to grazing angle. Only impenetrable surfaces are considered. Some calculations are presented, and are used to compare with the small perturbation, or Rayleigh–Rice theory. It is found that for near grazing incidence, Neumann boundary condition, the small perturbation theory gives inaccurate values, especially near the backscatter direction.