This paper proposes a novel multimodal deep weakly-supervised learning framework, SinkholeNet, to classify and localize sinkhole(s) in high-resolution RGB-slope aerial images. The SinkholeNet first employs a multimodal Convolutional Neural Network (CNN) architecture that simultaneously extracts features from the input RGB image and ground slope map and then fuses the extracted features. It then uses an improved ShuffleNet architecture on the fused features to classify patches as sinkholes or non-sinkholes. Finally, the last extracted feature maps, belonging to the sinkhole class, are used as input of gradient-weighted class activation mapping (Grad-CAM) to localize sinkhole(s) in a weakly-supervised setting. The proposed weakly-supervised framework intends to increase the available labeled data for training and decrease the cost of human annotation. We also introduce a novel publicly available weakly labeled sinkhole dataset comprising RGB-slope paired image patches to support reproducible research. The experimental results on the newly introduced dataset show that the SinkholeNet outperforms the other methods considered in this paper both for sinkhole classification and localization. © 2023 National Authority of Remote Sensing & Space Science