The deep-sea submersible is an essential piece of equipment for deep-sea development, serving as a crucial tool for conducting exploration and operations in the deep ocean. As the core component of the hydraulic system, the plunger pump is vital for ensuring the smooth lifting and lowering of the submersible. The plunger pair, which constitutes the most significant friction pair in plunger pumps, plays a pivotal role in determining both the service life and volumetric efficiency of the pump through its friction, lubrication, and sealing performance. This article proposes a flow model for the plunger pair in eccentric and inclined positions, considering its various orientations and placements. It elucidates the deformation and leakage characteristics of the plunger pair under different configurations, including various postures, material properties, and design parameters. The findings not only provide a theoretical foundation for the design of reciprocating seals and the evaluation of sealing performance but also contribute to the broader field of parameter design and performance assessment for other types of gap seals.