This paper introduces non-manifold offsetting operations, which add or remove a uniform thickness from a given non-manifold model. Since these operations can be applied to not only solids but also wireframe or sheet objects, they are potentially useful for pipeline modeling, sheet metal and plastic part modeling, tolerance analysis, clearance checking, constant-radius rounding and filleting of solids, converting of abstracted models to solids, HC too1 path generation and so on. This paper describes mathematical properties and algorithms for non-manifold offsetting. In this algorithm, a sufficient set of tentative faces are generated first by offsetting all or a subset of the vertices, edges and faces of the non-manifold model. And then they are merged into a model using the Boolean operations. Finally topological entities which are within offset distance are removed. The partially modified offsetting algorithms for wireframes or sheets are also discussed in order to provide more practical offset models.