Abstract: The multi-transmitting boundary condition has been generalized using spaceextrapolation to improve accuracy of the boundary condition in the time domain computa-tion. Refiection coefficients of the boundary in the frequency domain are formulated for twocases, in which the total wave fields are composed of the incident wave only and the incidentwave plus the fully developed refiecti on wave,respectively. The reflection coefficients arethen analyzed from a viewpoint of accuracv of the boundary in the time dom...