Slicing a model (computing thin slices of a geometric or volumetric model with a sweeping plane) is necessary for several applications ranging from 3D printing to medical imaging. This paper introduces a technique designed to compute these slices efficiently, even for huge and complex models. We voxelize the volume of the model at a required resolution and show how to encode this voxelization in an out-of-core octree using a novel Sweep Encoding linearization. This approach allows for efficient slicing with bounded cost per slice. We discuss specific applications, including 3D printing, and compare these octrees’ performance against the standard representations in the literature.