Recent advancements in neural 3D representations, such as neural radiance fields (NeRF) and 3D Gaussian splatting (3DGS), have made accurate estimation of the 3D structure from multiview images possible. However, this capability is limited to estimating the visible external structure, and it is still difficult to identify the invisible internal structure hidden behind the surface. To overcome this limitation, we address a new task called structure from collision (SfC), which aims to estimate the structure (including the invisible internal one) of an object from the appearance changes at collision. To solve this task, we propose a novel model called SfC-NeRF, which optimizes the invisible internal structure (i.e., internal volume density) of the object through a video sequence under physical, appearance (i.e., visible external structure)-preserving, and key-frame constraints. In particular, to avoid falling into undesirable local optima owing to its ill-posed nature, we propose volume annealing, i.e., searching for the global optima by repeatedly reducing and expanding the volume. Extensive experiments on 60 cases involving diverse structures (i.e., various cavity shapes, locations, and sizes) and various material properties reveal the properties of SfC and demonstrate the effectiveness of the proposed SfC-NeRF.