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Searching for objects in indoor organized environments such as homes or offices is part of our everyday activities. When looking for a target object, we jointly reason about the rooms and containers the object is likely to be in; the same type of container will have a different probability of having the target depending on the room it is in. We also combine geometric and semantic information to infer what container is best to search, or what other objects are best to move, if the target object is hidden from view. We propose to use a 3D scene graph representation to capture the hierarchical, semantic, and geometric aspects of this problem. To exploit this representation in a search process, we introduce Hierarchical Mechanical Search (HMS), a method that guides an agent's actions towards finding a target object specified with a natural language description. HMS is based on a novel neural network architecture that uses neural message passing of vectors with visual, geometric, and linguistic information to allow HMS to reason across layers of the graph while combining semantic and geometric cues. HMS is evaluated on a novel dataset of 500 3D scene graphs with dense placements of semantically related objects in storage locations, and is shown to be significantly better than several baselines at finding objects and close to the oracle policy in terms of the median number of actions required. Additional qualitative results can be found at https://ai.stanford.edu/mech-search/hms.