The molecular crystal s-triazine, C3N3H3, is known to undergo a transition from a trigonal to a monoclinic structure when cooled below Tc=200K. Inelastic neutron scattering measurements have been carried out on a single crystal of s-triazine at various temperatures. A pronounced softening of transverse modes governed by the elastic constant c 44 is observed in the vicinity of Tc. The phonon response remains underdamped at energies down to at least 0.07 meV and no 'central peak' is observed. The transition seems to be slightly first order ('quasi-continuous') in accordance with recent observations, while it has been reported to be of second order at higher pressures.