Earlier we reported the fabrication of a model superoleophobic surface comprising ∼3 μm diameter pillar arrays (height ∼7.8 μm, pitch 6 μm) on silicon wafer via the conventional photolithography and surface fluorosilanation techniques. Results showed that both surface fluorination and the re-entrant structure in the pillar are crucial in achieving superoleophobicity and superhydrophobicity with hexadecane and water contact angles exceeding 150° and sliding angles at ∼10°. In this work, we investigate design parameters for the fabrication of a superoleophobic surface that is robust against wetting breakthrough pressure and mechanical abrasion. By studying the effects of pillar height, size and spacing, we show that both static and advancing contact angles remain "super" (>150°) as the pillar size and spacing vary, the receding contact angle, sliding angle and contact angle hysteresis, on the other hand, are found to be sensitive to these structural changes. The receding angle decreases and both sliding angle and hysteresis increase as the solid area fraction increases. Interestingly, surface superoleophobicity remains as the height of the pillar decreases from ∼7.8 to 1 μm. Surface Evolver simulation was used to model the location of the contact line as well as the robustness in wetting against external pressure. The abrasion resistance of the pillar array surface was assessed by mechanical modeling and nanoindenter measurement. The design space for fabricating a mechanically robust superoleophobic surface is discussed.