The probleм of reconstructing the two–dimensional distributions of the attenuation and backscattering coefficients from the data of the airborne tomographic sounding of the atmosphere is considered. Solutions of the integral equations of two–beam and three–beam tomographic lidar sounding have been obtained analytically. It has been shown that in this case it is not unnecessary to use any a priori assumption regarding the characteristics sought for to reconstruct the attenuation and backscattering coefficients. The solutions obtained in this paper can serve as the basis for the construction of new calculational algorithms for tomographic laser sounding of the atmosphere.