As a calculation method of road traffic noise at the roadside area of a semi-underground road, the “hypothetical point source method” was proposed in the road traffic noise prediction model “ASJ RTN-Model” proposed by the Acoustical Society of Japan. In this method, noise radiation from a straight semi-underground road is simply modeled as sound propagation from a hypothetical point source that has a directivity specific to the dimensions of the structure and is assumed to be at the center of the mouth. In the ASJ RTN-Model 2003, the directivity characteristics were determined on the basis of the results of a scale model experiment, and the variation of the applicable dimensions of the road structures was limited. In this paper, the directivity characteristics of the hypothetical point source are examined by wave-based numerical analysis to extend the variation. In the numerical analysis, a Fourier-type transformation technique from a two-dimensional field to a three-dimensional field is applied to the calculation results obtained by the two-dimensional finite-difference time-domain method. In addition, the practical expression of the sound power of the hypothetical sound source is investigated.