Information loss induced by digitization is inevitable, and constitutes a classical problem in digital geometry. Indeed, preserving the geometric and topological features of an object is crucial for image processing tasks. To ensure this preservation when converting continuous objects to discrete representations, different classes of shapes have been introduced. However, the current state of the art still leaves room for the definition of non smooth classes that have digitization preservation properties. To that end, we focus on Locally Turn-Bounded (LTB) Curves, introduced by É. Le Quentrec et al. in 2019. While LTB curves has shown promising results in two dimensions, their extension to higher dimensions is not trivial. This paper introduces the Locally Turn-Bounded Surfaces, a generalization of LTB curves to the 3D Euclidean space. As first results, we not only show that our definition preserves basic properties from LTB curves to LTB surfaces, but also demonstrate that LTB surfaces impose conditions on topology, notably preventing the surface from containing small holes.