Two-dimensional layered trichalcogenide materials have recently attracted the attention of the scientific community because of its robust mechanical, thermal properties and applications in opto and nanoelectronics devices. We report the pressure dependence of out-of plane Ag Raman modes in high quality few-layers titanium trisulfide (TiS3) nanoribbons grown using a direct solid-gas reaction method and infer their cross-plane thermal expansion coefficient.Both mechanical stability and thermal properties of the TiS3 nanoribbons are elucidated using phonon-spectrum analyses. Raman spectroscopic studies at high pressure (up to 34 GPa) using a diamond anvil cell identify four prominent Ag Raman bands; a band at 557 cm-1 softens under compression, and others at 175, 300, and 370 cm-1 show normal hardening. Anomalies in phonon mode frequencies and excessive broadening in line-width of the soft phonon about ~ 13 GPa are attributed to the possible onset of a reversible structural transition. A complete structural phase transition at 43 GPa is inferred from Ag soft mode frequency (557 cm-1) versus pressure extrapolation curve, consistent with recent reported theoretical predictions. Using the experimental mode Gr\"uneisen parameters i of Raman modes, the cross-plane thermal expansion coefficient Cv of the TiS3 nanoribbons at ambient phase is estimated to be1.32110-6K-1. The observed results are expected to be useful in calibration and performance of next generation nano-electronics and optical devices under extreme stress conditions.