The Cherenkov Telescope Array (CTA) consortium aims to create the next generation Very High Energy gamma-ray observatory. It will be devoted to the observation of gamma rays over a wide band of energy, from 20 GeV to 300 TeV. Three different classes, Large, Medium and Small Size Telescopes, are foreseen to cover the low, intermediate and high energy regions, respectively. The energy range of the Small Size Telescopes (SSTs) extends from 1 TeV to 300 TeV. Among them, the Gamma-ray Cherenkov Telescope (GCT), a telescope based on a Schwarzschild-Couder dual-mirror optical design, is one of the prototypes under construction proposed for the SST sub-array of CTA. This contribution focuses on the mechanical structure of GCT. It reports on last progress on the mechanical design and discusses this in the context of CTA specifications. Recent advances in the assembly and installation of the opto-mechanical prototype of GCT on the French site of the Paris Observatory are also described.