Abstract: A computing model is presented for the calculation of the transient population distribution of polyatomic molecules excited by an IR laser pulse, SF_6 has been used as an example. This model allows the calculation of the vibrational energy distributions from the observed IR fluorescence or absorption spectrum, and vice versa. The thermal vibrational distribution calculated by this model from the mea- sured spectrum of SF_6 at 300 K is in good agreement with the Boltzmann distribu- tion (Table 1). The present model has a few advantages over an earlier study~[1], such as higher precision of computation, accurate generation of the vibrational transition matrix and being capable of calculating the transient vibrational population distribution at any instant after laser excitation. Using this model a rotationally resolved spectrum of SF_6 at 20 K has been obtained for the first time.