The Search for Hidden Particles (SHiP) experiment is a new general-purpose fixed target facility proposed at the CERN Super Proton Synchrotron (SPS) accelerator to search for long-lived exotic particles associated with Hidden Sectors and Dark Matter. This paper reports on the structural design of SHiP’s decay volume, a > 2000 m3 conical vessel under vacuum that should host several large particle physics detector systems. In the field of structural and seismic engineering, the design study in a very multidisciplinary international collaboration has represented a stimulating research challenge. The goal of the design of the decay is to produce a structure as light and as slim as possible to stay within the geometrical envelop determined in the physics simulations. A complete study has been performed with all the steps from the conceptual design, including the interaction with other components and the plant systems, to the assembly procedures for the decay volume realization. The complexity of the case study has been driven by the need of finding the appropriate compromise between the physics performance, the structural aspects, the executive, constructive and operational issues, and the economical constraints. The assembly strategy, the welding techniques, and the expected construction time are discussed in view of the extremely complex installation phase. Building Integrated Model (BIM) methodology is also proposed as an essential tool to coordinate the entire process of designing and managing not only the decay volume but the entire project.