An analysis is presented of some specific features of short optical pulses propagating along the slant paths in a resonantly absorbing medium. Results are obtained for the model of an inhomogeneous, vertically stratified medium in the geometrical optics approximation. It has been shown that the inertia of response of the resonant medium has an appreciable effect on the propagation process so that both the pulse shape and the energy parameters of the beam depend on the direction of propagation