Soft elastohydrodynamic lubrication (EHL) problems widely exist in hydraulic reciprocating rod seals and pose great challenges because of high nonlinearity and strong coupling effects, especially when the EHL problems are of high dimensions. In this paper, a strongly coupled fluid structure interaction (FSI) model is proposed to solve the transient soft EHL problems in U-cup hydraulic reciprocating rod seals. The Navier–Stokes equations, rather than the Reynolds equation, are employed to govern the whole fluid field in the soft EHL problems, with the nonlinearity of the solid taken into consideration. The governing equations of the fluid and solid fields are combined into one equation system and solved monolithically. To determine the displacements of nodes of the fluid field, a new moving mesh method based on the combination of the Laplace equation and the leader–follower methods is put forward. At last, the proposed FSI model runs successfully with the moving mesh method, and the boundaries of the hydrodynamic lubrication zones and the hydrostatic zones are formed automatically and change dynamically during the coupling process. The results are as follows: The soft EHL problems show typical characteristics, like the constriction effects of the lubricating films, and the law of dynamic development of the lubricating films and the fluid pressures is revealed. The minimum stroke lengths needed to generate complete lubricating films vary with the rod speeds and movement directions, so the design of the rod seals should be paid close attention to, in particular the rod seals of short stroke lengths. Furthermore, along with the dynamic development processes of the fluid pressures during the instroke of U-cup seals, the lubricating film humps expand and locate between the fluid pressure abrupt points and the outlet zones. After the U-cup seals reach the steady-states, the fluid abrupt points disappear and no changes of the film humps are observed. Theoretically, the proposed method can be popularized to solve similar soft EHL problems.