The concept of body and subbodies is fundamental in mechanics. Fit regions are those sets in an Euclidean space which can be occupied by continuous bodies and their subbodies. General considerations show among other things that the union of two subbodies should be a subbody and that a subbody should have a boundary and a well defined normal vector field on that boundary. In an earlier paper by \textit{M. E. Gurtin, W. O. Williams} and \textit{W. P. Ziemer} [ibid. 92, 1-22 (1986; Zbl 0599.73002)] it was shown that the class of sets of finite perimeter satisfies the requirements for fit regions. (A measurable set \(A\subset {\mathbb{R}}^ n\) has finite perimeter if the distributional gradient grad \(ch_ A\) of the characteristic function \(ch_ A\) of A is a vector valued Radon measure of finite variation.) In the paper under review the authors show that the class of sets of finite perimeter is unnecessarily large and propose instead the following definition: A subset \(D\subset {\mathbb{R}}^ n\) is a fit region in \({\mathbb{R}}^ n\) if it (i) is bounded, (ii) is regularly open, (iii) has finite perimeter, (iv) the topological boundary of D has volume-measure zero. In the first four sections of the paper analytical tools are presented. In section five fit regions are introduced as above and several stability properties of the class of fit regions are proved. In section six the reduced boundary Rby(A) of a fit region A is defined as the set of points \(x\in {\mathbb{R}}^ n\) where there exists an outer normal to A in the measure theoretic sense. Several enlightening examples are presented in the final section seven.