The classical trajectory approach has been used to study the shock wave-induced desorption of a model triatomic linear adsorbate from a variety of model surfaces to which it is weakly adsorbed. The branching fraction among intact adsorbate desorption, fragmentation, and desorption with fragmentation has been analyzed as a function of shock wave energy, Debye frequency of the lattice, and the frequency and dissociation energy of the weak terminal interadsorbate bond. In general, fragmentation (with or without desorption) was observed to dominate over intact desorption. The results are explained partially in terms of resonances between low frequency adsorbate modes and the Debye frequency of the lattice. In addition, no evidence was found for a bottleneck in intact desorption which would allow the desorbing molecule to remain internally cold.