This study establishes a flow-induced nonlinear vibrations (FINV) model of tubing string using micro-finite element and energy methods along with the Hamilton variational principle. This model helps address the wear failure of tubing strings caused by FINV in high-pressure, high-temperature, and high-yield (3H) gas wells and considers the changes in wellbore trajectory, wellbore temperature/pressure, and contact/collision of the tubing-casing. To validate the proposed model, a simulation experiment of tubing string vibration was conducted. Based on the White-Fleisher wear theory, a method is proposed for calculating wear amount and depth of tubing string in 3H gas wells; the friction coefficient and wear rate are determined via a wear experiment. Thus, the influences of production rate, inclination angle, well section length, packer position, and centralizer position on the wear characteristics of tubing string are systematically analyzed. The results obtained demonstrate that, first, with the increase of production rate, the wear life of the tubing string decreases, and there exists a sudden value of production rate, which can be determined using the proposed analysis method, such that the field production allocation should be far away from the sudden production rate. Second, in the well trajectory design, the vertical section length should be small, while that of build-up section and the angle of stable inclined section should be large. Third, the optimal positions for the packer and centralizer in the field depend on the well structure, downhole tool size, etc. and can be determined using the proposed analysis method; these positions help design field tools. The research results provide a theoretically sound guidance for designing and practically sound approach for effectively improving the service life of tubing string in 3H gas wells.