LiteBIRD is a JAXA strategic L-Class mission designed to search for the existence of primordial gravitational waves produced during the inflationary phase of the Universe. This is achieved through measurements of their imprint on the polarization of the cosmic microwave background (CMB). To fulfill the scientific objectives, observations have to be made over a wide range of frequencies (34 GHz - 448 GHz), which is accomplished by three telescopes: the Low-Frequency Telescope (LFT) led by JAXA and the Middle & High-Frequency Telescopes (MHFT) under European responsibility and led by CNES. To withstand the launch, comply with satellite requirements, and minimize the mass of the mechanical structure, we conducted finite element modeling of the entire MHFT, incorporating both modal and quasi-static load analyses. A nodal thermal study was carried out to evaluate, on the one hand, the static thermal loads of the instruments, and on the other hand the sensitivity of the instruments to sinusoidal disturbances simulating those caused by the ADR cooling system. This paper outlines the methodology employed in designing the mechanical structure of the MHFT, then summarizes the initial results and conclusions drawn from various mechanical and thermal analyses performed on the MHFT.