Visual object counting is a fundamental computer vision task underpinning numerous real-world applications, from cell counting in biomedicine to traffic and wildlife monitoring. However, existing methods struggle to handle the challenge of stacked 3D objects in which most objects are hidden by those above them. To address this important yet underexplored problem, we propose a novel 3D counting approach that decomposes the task into two complementary subproblems - estimating the 3D geometry of the object stack and the occupancy ratio from multi-view images. By combining geometric reconstruction and deep learning-based depth analysis, our method can accurately count identical objects within containers, even when they are irregularly stacked. We validate our 3D Counting pipeline on large-scale synthetic and diverse real-world datasets with manually verified total counts.