A series of lower-bound adaptive finite element limit analyses (LB-AFELA) was performed to compute the ultimate bearing capacity of a rigid rough strip footing situated on the crest of a rock slope with an underground circular void. The generalized Hoek–Brown criterion was utilized. The results were presented using a dimensionless bearing capacity factor (), considering various void locations, rock slope strength properties, and slope angles. Furthermore, an in-depth investigation was carried out to evaluate the formation of the failure patterns beneath the strip footing on the rock slope, considering an underground circular void. A comparison was made to assess the precision of the obtained results for a rigid rough strip footing at the edge of the rock slope between the LB-AFELA and stress characteristics method. The results showed that as the circular void moved further away from the strip footing, the , increased until the influence of the circular void faded. The interaction between the strip footing, rock slope, and the circular void resulted in a combined failure mechanism involving roof and bearing capacity failure.