The scattering by a hole/aperture within a perfect electric conducing (PEC) plane is a classical electromagnetic problem. As is well known, this scattering can be formulated as the solution of an integral equation where the unknown aperture electric field (or equivalently the magnetic source) is to be retrieved once the incident field is known. When the aperture becomes a hole small in terms of the wavelength, Bethe’s diffraction theory [1] or the low frequency approximation (Stevensons series low order terms) [2] can be invoked to approximate the mentioned integral equation. This allows getting analytical results for simple hole’s shape, for example in the case of circular hole. For such a case, in this paper, analytical results are compared with numerical simulations obtained by a commercial FDTD forward solver. It is shown that in near zone, low-frequency approximation fits numerical simulations better than the Bethe’s theory does. By contrary, Bethe’s theory works fairly well in predicting the radiated field in far-zone and allows to obtain a more handling field expression which in principle permits to more easily considering the role of the incident field polarization and the hole’s shape. Finally, the case of a hole over the faces of a rectangular waveguide located at different points is analyzed as well. It is found out that Bethe’s theory works also in these cases.