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This study proposes a three-dimensional upper bound solution for estimating the soil thrust of tracked vehicles on saturated clay slopes. The present study considered block, triangular wedge, and trapezoidal wedge failure modes to formulate an upper bound solution for each. The analytical solution for soil thrust was determined as the minimum upper bound solution among those for each failure mode. This analytical solution was validated through numerical simulations that modeled track-ground interactions. Parametric studies, based on the upper bound solution, assessed the impact of track system shape, vehicle weight, undrained shear strength, and ground slope on soil thrust. The analytical solutions and parametric studies provide a rapid method for assessing vehicle operability on clay slopes and offer references for designing tracked vehicles suitable for site conditions.