This paper deals with the bearing capacity determination of strip footing on a rock mass in hilly area by considering the influence of inclined and eccentric loading. Applying the generalized Hoek-Brown failure criterion, the failure behavior of the rock mass is modeled with the help of the power cone programming in the lower bound finite element limit analysis framework. Using bearing capacity factor (Nσ), the change in bearing capacity of the strip footing due to the occurrence of eccentrically inclined loading is presented. The variations of the magnitude of Nσ are obtained by examining the effects of the Hoek-Brown rock mass strength parameters (uniaxial compressive strength (σci), disturbance factor (D), rock parameter (mi), and Geological Strength Index (GSI)) in the presence of different magnitudes of eccentricity (e) and inclination angle (λ) with respect to the vertical plane, and presented as design charts. Both the inclined loading modes, i.e., inclination towards the center of strip footing (+λ) and inclination away from the center of strip footing (−λ), are adopted to perform the investigation. In addition, the correlation between the input parameters and the corresponding output is developed by utilizing the artificial neural network (ANN). Additionally, from sensitivity analysis, it is observed that inclination angle (λ) is the most sensitive parameter. For practicing engineers, the obtained design equation and design charts can be beneficial to understand the bearing capacity variation in the existence of eccentrically inclined loading in mountain areas.