A method for analyzing the three-directional coupled dynamic response of wind-excited buildings is presented. The method is based on a random vibration concept and is parallel to those currently used for analyzing alongwind response. Only the buildings with rectangular cross-section and normally-incident wind are considered. The alongwind pressures and their correlations are represented by the well-known expressions that are available in the literature. The acrosswind forces are assumed to be mainly due to vortex shedding. The torque acting on the building is taken as the sum of the torque due to random alongwind forces plus the torque due to asymmetric acrosswind forces. The study shows the following: (1) amplitude of acrosswind vibrations can be several times greater than that of alongwind vibrations; (2) torsional vibrations are significant if the building has large frontal width, and/or it is asymmetric, and/or its torsional natural frequency is low; (3) even a perfectly symmetric structure with normally incident wind can experience significant torsional vibrations due to the randomness of wind pressures. ?? 1987.