Very high resolution satellite images can be used to generate stereoscopic digital elevation models (DEMs), efficiently and at scale, as exemplified by the upcoming CO3D mission, which aims to produce worldwide DEMs by the end of 2025. In this paper we present a deep learning stereo-vision algorithm, integrated in the Stereo Pipeline for Pushbroom Images (S2P) framework. The proposed stereo matching method applies a Siamese convolutional neural network (CNN) to construct a cost volume. A median filter is applied to every slice in the cost volume to enforce spatial smoothness, and another CNN estimates a confidence map which is used to derive the final disparity map. Simulation results on the IARPA dataset show that the proposed method improves completeness by 4.5%, compared to the state of the art. A qualitative assessment also shows that the proposed method generates DEMs with less noise.