Abstract In recent years, 3D data has been widely used in archaeology and in the field of conservation and restoration of cultural properties. Virtual restoration, which reconstructs the original state in virtual space, is one of the promising applications utilizing 3D scanning data. Though many studies of virtual restoration have been conducted, it is still challenging to restore the cultural properties that consist of multiple deformable components because it is not feasible to identify the original shape uniquely. As a solution to such a problem, we proposed a non-rigid 3D shape assembly method for virtually restoring wooden ships that are composed of multiple timbers. The deformed timber can be well represented by ruled surface. We proposed a free-form deformation method with a ruled surface and an assembly method to align the deformable components mutually. The method employs a bottom-up approach that does not require reference data for target objects. The proposed framework narrows down the searching space for optimization using the physical constraints of wooden materials, and it can also obtain optimal solutions. We also showed an experimental result, where we virtually restored King Khufu’s first solar boat. The boat was originally constructed by assembling several timbers. The boat was reconstructed as a real object and is currently exhibited at a museum. However, unfortunately, the entire shape of the boat is slightly distorted. We applied the proposed method using archaeological knowledge and then showed the virtual restoration results using the acquired 3D data of the boat’s components.