In this work the diffraction problem of an electro-magnetic field by the plane-parallel waveguide aperture is solved by the uniform asymptotic theory of diffraction (UАТ). The problem is reduced to the solution of the model problem – diffraction between two perfectly conducting half-planes. The solution found is valid both at the distance and near the shadow boundaries of the incident and reflected fields. In the distance it turns into the solution of the geometrical theory of diffraction (GТD). However it is not determined close to edges and other caustics.