A Very High Temperature Gas Cooled Reactor (VHTR) has been selected as a high energy heat source of the order of $950^{circ}C$ for nuclear hydrogen generation, which can produce hydrogen from water or natural gas. A primary hot gas duct (HGD) as a coaxial double-tube type cross vessel is a key component connecting a reactor pressure vessel and an intermediate heat exchanger in the VHTR. In this study, a structural sizing methodology for the primary HGD of the VHTR is suggested in order to modulate a flow-induced vibration (FIV). And as an example, a structural sizing of the horizontal HGD with a coaxial double-tube structure was carried out using the suggested method. These activities include a decision of the geometric dimensions, a selection of the material, and an evaluation of the strength of the coaxial double-tube type cross vessel components. Also in order to compare the FIV characteristics of the proposed design cases, a fluid-structure interaction (FSI) analysis was carried out using the ADINA code.