Existing volumetric representations model a non- thickness surface using voxels, and thus cannot accurately manipulate topology changes in the interactions between surfaces and solids. This study describes a volume repre-sentation in which face flags and distance-levels on each voxel represent surface topology and geometry, and an object flag identifies solids. Also presented herein is a set of algorithms that voxelize solids and surfaces, check the closures of the interactions among the volumetric surfaces and solids and manipulate various operations on the solids. A surgical example, in which the procedures involved in the complex interactions between cutting surfaces and anatomic structures and various geometric and topologic manipulations on the structures, are simulated to demon-strate that these novel volume representation and algo-rithms are feasible in manipulating the interactions be-tween surfaces and solids in a volume.