The long-term safety of pressure-resistant structures used in deep-sea equipment may be threatened by creep deformation. The creep deformation behavior of a pressure-resistant structure made of different titanium alloys, Ti-6Al-4V and Ti-4Al-2V, at room temperature is investigated in this research. The kinetics and mechanisms underlying creep deformation in these materials is explained by proposing an improved constitutive model considering the effects of stress level, loading rate and environmental temperature field, offering crucial information for optimizing design parameters and guaranteeing the lifespan of the structure. Model parameters are determined for the two types of titanium alloys based on tensile creep testing results and validated through a simulation of the experimental process. In this study, a material creep model was used to predict the long-term deformation of large pressure-resistant titanium structures to ensure safe long-term operation. The safety factor used in the model is 1.5. Finite element analyses are conducted for the creep behavior of the pressure-resistant structure under real operating circumstances based on the creep constitutive model. The simulation predicts stress distribution, strain evolution, and deformation size over long periods of time by integrating complicated geometries, boundary conditions, and material characteristics. The present research can provide basic information for the local impacts of creep deformation on the inside of facilities, which helps refine design strategies to reduce possible damage risks.