<p>A parametric study was conducted to evaluate the undrained bearing capacity of rigid footings on homogeneous clay slopes using a newly developed Rigid Plastic Finite Element Method (RPFEM) code. To prevent unrealistic tensile stresses within the soil, a zero-tension analysis was introduced to model the footing–slope contact under eccentric and inclined loads. The analysis investigated the effects of both positive and negative eccentricities, caused by the asymmetry of the slope, and considered slope parameters such as slope angle (<i>α</i>), slope height (<i>h</i>), and footing setback (<i>S</i>), alongside key soil properties including undrained shear strength (<i>c</i>_u) and unit weight (γ). The proposed method provided a comprehensive understanding of the undrained failure envelope in vertical force (<i>V</i>), horizontal force (<i>H</i>), and moment (<i>M</i>) space. The influence of both positive and negative horizontal loads on the undrained failure envelope (<i>V–H–M</i>) was examined, revealing the significant role of eccentricity and horizontal load direction in shaping failure mechanisms. The findings underscored the effectiveness of the zero-tension analysis in capturing the interaction between the footing base and soil surface, leading to the derivation of new failure envelope equations across a wide range of <i>c</i>_<i>u</i>, <i>α</i>, and <i>S</i>. The applicability of the undrained failure envelope across various loading paths was comprehensively examined, demonstrating its consistency with different slope geometries and soil properties.</p>