Pillar width analysis is an important design component of multiple underground openings. Due to high costs associated with the design of underground oil storage caverns, the establishment of several parallel caverns in necessary to ensure adequate oil storage capacity and production. Hence, development of guidelines and design methodologies are beneficial in the design of rock pillars in underground oil storage technology. In this work, a comprehensive numerical analysis was carried out to determine the appropriate pillar width in an unlined rock cavern facility. Four identical parallel caverns of 28 m (span) × 35 m (height) at a depth of 100 m were simulated using the 3D finite difference method. A 32 m ground water level was assumed above the caverns roof. The full stress and displacement fields were computed numerically for varying pillar widths. The behavior and failure mechanism of pillars between caverns were analyzed. The analysis results show that the side cavern displacement fields are not symmetric, but for the central caverns the wall displacement is fairly symmetric. Based on numerical findings, and with regard to the results presented in the paper, in multi-cavern underground oil storage environment an inter-cavern pillar width of 1.1–1.3 times the cavern span is a safe pillar width.