Some peculiarities of attenuation of laser pulses during their propagation in a resonantly absorbing medium over slant and vertical atmospheric paths are analyzed in the paper. A plane-layered atmospheric model is considered. Calculations take into account the altitude variations of shape, width, and center of an absorption line and the concentration of an absorbing gas. The transmission of the medium is examined as a function of the radiation propagation direction. The influence of the absorption line center shift due to air pressure on this parameter is also considered. The estimates have been obtained for laser generation lines in the spectral region of the atmospheric water vapor absorption.