Surface texture shape significantly influences the tribological and sealing properties of fluid mechanical face seals. Considering that it is a contradiction to simultaneously improve load capacity and reduce leakage, a numerical multi-objective optimization model is proposed herein to improve the load-carrying capacity while reducing the volume leakage rate via texture shape optimization. The mass-conserving cavitating boundary condition and the non-dominated sorting genetic algorithm II are employed for the optimization. The numerical results indicate that the optimal texture shape is spiral-like under the lowest volume leakage rate, which becomes an asymmetric flat-front chevron with increasing load-carrying capacity and volume leakage rate. The optimal shape outperforms four regular shapes (all obtained by multi-objective optimization) at different rotation speeds and sealing pressures. The cavitation within the optimal shape ensures zero leakage in fluid face seals. The comprehensive performance of the texture shape obtained by multi-objective optimization is superior to that obtained by single-objective optimization.