Machine hammer peening (MHP) is an incremental surface finishing process. It enables both surface smoothing and texturing. Compared to well-established surface texturing processes, MHP has the advantage of simultaneous induction of strain hardening and compressive residual stresses. Both texturing and surface layer modification are very beneficial in case of mixed-boundary lubrication. MHP has been only recently developed. Therefore, the influence of surface textures manufactured by MHP on tribological interactions is unknown and lacks fundamental investigations. In this work, hydrodynamics of MHP textures is investigated by means of a three-dimensional (3D) computational fluid dynamics (CFD) analysis. The analyzed MHP textures have already been experimentally used to reduce friction in strip drawing tests. Using CFD analysis, an optimal arrangement of multiple elliptically shaped surface structures for maximizing the fluid pressure and the load-bearing capacity is determined. Furthermore, a correlation between the determined process parameters and the lubrication properties is presented. Because of significantly high hydrostatic pressures, cavitation is neglected in this work. Additionally, the effect of structure pileups is neglected in this study. Within the range of parameters investigated, it was found that an arrangement of surface textures by MHP should be transversally overlapping and clearly separated longitudinally. High structure depths, lubricant viscosities, and sliding velocities further improve the load-bearing capacity as well as small fluid-film thicknesses.