This paper presents a surface and solid voxelization approach for incomplete point cloud datasets. Voxelization stands for a discrete approximation of 3-D objects into a volumetric representation, a process which is commonly employed in computer graphics and increasingly being used in computer vision. In contrast to surface voxelization, solid voxelization not only set those voxels related to the object surface but also those voxels considered to be inside the object. To that end, we first approximate the given point set, usually describing the external object surface, to an axis-aligned voxel grid. Then, we slice-wise construct a shell containing all surface voxels along each grid-axis pair. Finally, voxels inside the constructed shell are set. Solid voxelization results from the combination of all slices, resulting in a watertight and gap-free representation of the object. The experimental results show a high performance when voxelizing point cloud datasets, independently of the object's complexity, robust to noise, and handling large portions of data missing.