The article is devoted to creating a refined computer model of the face packing seal (FPS) based on the solution of the two-way fluid-structure interaction (2-way FSI) problem. An approach to the average gap was proposed based on the micro-space’s working medium leakage between the friction pair’s roughness elements. Three FPS designs were studied, in which the following operating parameters were alternately changed: inlet pressure, load factor, stuffing box parameters, and friction coefficient. Young’s modulus, Poisson’s ratio, and the thickness of the annular plate at the bottom of the stuffing box were also changed. The model was created considering the actual geometry of the FPS. The shaft rotation was considered by applying the rotation condition on the wall of the fluid model. The calculation was carried out using the ANSYS Multiphysics software. The results of the calculations were presented in the form of graphic dependences with a comparison of the hydrostatic and contact pressure distributions over the friction pair width. The values of the magnitudes of leakage from the changing parameters were presented. Based on the obtained results, an optimal combination of parameters was evaluated for the most efficient design of the FPS.