Radio acoustic sounding system (RASS) is a detection technique using the interaction between radio wave and acoustic wave to remotely measure vertical profiles of the atmospheric temperature, and usually composed of a Doppler radar with fixed beam (monostatic or bistatic) and an acoustic source with high power. By combining acoustic propagation equation and radio wave propagation equation in a disturbance medium and using a finite-difference time-domain method, a numerical model describing the interaction between acoustic wave and electric wave is constructed, and the model is used to analyze the effects of wind and temperature on detection height of RASS. In the atmospheric temperature background, the propagations of a single frequency acoustic wave packet under different wind conditions are simulated, and the scattering propagation of electric wave packets corresponding to the acoustic scatterer are analyzed and compared. Besides, the entire physical process are described from the angle of energy density. The numerical simulation results show that the propagation trajectories of both acoustic wave and radio wave backscattering echo are changed due to the existence of wind field and temperature profile. The presence of wind field results in an offset of acoustic wave front, reducing the strength and changing the trajectory of radio wave backscattering echo, so that the detection height is limited due to the reduction of receiving data. The simulation results of the acoustic wave reveal that the temperature profile mainly affects the propagation velocity of acoustic wave, while the presence of wind field may result in shifts of propagation trajectory and acoustic wave front, and the greater the wind speed, the more the horizontal shift of acoustic wave front is. The numerical analyses of scattering propagations of radio wave with the acoustic scatterer at the same height under different background atmospheric conditions manifest that the stronger the wind speed, the more the deviation of electric wave echo from the receive antenna is, and the smaller the echo intensity is when the scattering echo propagates to the same position. The theoretical calculations with the acoustic wave scatterer at different heights under the same atmospheric wind field (strong wind) background demonstrate that if the height of scattering point is reduced, the offset of the scattering echo “bunching point” at the same altitude will be greatly improved and the intensity will be enhanced, but it also means the decline of detection height. In order to improve the detection height under the background of wind field, some methods are adopted, such as using a bistatic radar antenna or increasing the reception antenna area.