This study proposes a novel methodology to compute the stability of a strip footing placed on a spatially varying rock mass. It incorporates the deep learning model—Convolutional Neural Network (CNN) in tandem with lower-bound random finite element limit analysis (LB-RFELA). A meta-model is developed to reduce the computational effort of using Monte Carlo Simulation (MCS), which is usually used in conjunction with FELA to incorporate anisotropic spatial variability in the rock mass. Spatially varying random fields of uniaxial compressive strength (σci) associated with the problem in this study are generated using RFELA and fed to the developed CNN model. CNN studies images thoroughly and predicts the stability number, Npred. After training CNN with a sufficient and adequate amount of random fields, it is used as a meta-model to formulate the stability of strip footing by extracting the spatial features from the complex random field images. Advanced features of the developed model alleviate the burden of cumbersome conventional approaches. An efficient CNN model with appropriate depth (convolution and pooling layers) is prepared to classify the simulation as failing {0} or not failing {1} (binary classification) about Ndet. The accuracy of CNN-predicted outputs is measured vis-à-vis the unlearnt RFELA predictions.