Fire accidents in oil tank farms can trigger domino effects, leading to multiple tank fires with catastrophic consequences. Preventing losses in large-scale tank farms requires a dynamic assessment of fire-induced domino accidents. Existing research often focuses on calculating the time to failure (TTF) of storage tanks but overlooks the influence of failure modes. This study develops numerical models to explore failure modes of oil storage tanks with uniform and stepwise walls exposed to thermal radiation. Factors such as the flame heights of combustion tank, adjacent spacings, wall thickness, and tank volumes are considered. The numerical model employs a solid double-layer flame model to determine thermal radiation intensity and temperature, followed by a dynamic stress–strain and buckling analysis to obtain time to buckling (TTB) and time to yielding (TTY). If TTB < TTY, the failure model is buckling; otherwise, the failure model is yielding. Results indicate that failure modes in nonuniform thermal fields include buckling and yielding, with stepwise walls favoring buckling and uniform walls favoring yielding. When the wall thickness is below the critical value, failure is yielding; otherwise, it is buckling. These findings support risk management and emergency response for fire-induced domino effects in oil tank farms.