Inspired by the analytical interest in matrix/analyte systems for static secondary ion mass spectrometry (s-SIMS), we report on classical molecular dynamics simulations of the 500-eV Ar-induced sputtering of samples composed of 2 kDa polystyrene oligomers embedded in a trimethylbenzene matrix. The statistics of the ejected species and the mechanistic analysis of representative trajectories help us understand the main features of molecular desorption for such matrix/analyte samples. Matrix molecules and clusters, but also analyte molecules and matrix/analyte clusters, are observed among the species ejected after 8.5 ps. The average emission depth of sputtered species decreases as a function of their size. The velocity distributions of analyte molecules and matrix/analyte clusters are centered at similar to400 m/s, which is comparable to MALDI observations. In parallel, the average velocity and internal energy of matrix molecules depend on their depth of origin under the surface, the internal versus kinetic energy ratio increasing with emission depth. The fraction of matrix molecules undergoing chemical reactions increases accordingly with depth. From the mechanistic viewpoint, large molecules and clusters are desorbed in a late stage of the interaction, after the energy initially carried by the atomic collision cascade has been transformed into collective vibrational excitations and molecular motions. These theoretical predictions are compared to experimental results, and routes to improve molecular desorption in s-SIMS are explored.