The semiclassical stochastic trajectory method is extended to the study of rotational and vibrational transitions for linear triatomic molecules colliding with non-rigid solid surfaces. Rotational and vibrational motion are treated by quantum mechanics, translational motion by classical mechanics, and surface atom motion by the classical generalized Langevin equation. Self-consistent coupling of all motions is enforced via Ehrenfest's theorem. Calculations of the kinetic energy and gas temperature dependence of trapping probabilities, vibrational relaxation probabilities and final vibrational state distributions are presented for the CO 2-Ag(111) system at surface temperatures of 0 and 600 K. The trapping probabilities are greatly enhanced by the rotational motion and also vary to some degree with the initial vibrational state of the CO 2. Total vibrationally inelastic probabilities are on the order of 10 -2 for a single collision event with an initial state (00°1). For the initial state (01 10) these are much larger, ~ 10 -1, due to the nature of bending mode motion. In conjunction with the large trapping probabilities, the mechanism of vibration to vibration, rotation, translation, phonon energy transfer can provide vibration relaxation probabilities in the range of those measured experimentally. A pseudo-selection rule for conservation of vibrational angular momentum is found.