In this paper we propose an object recognition approach that is based on shape masks--generalizations of segmentation masks. As shape masks carry information about the extent (outline) of objects, they provide a convenient tool to exploit the geometry of objects. We apply our ideas to two common object class recognition tasks--classification and localization. For classification, we extend the orderless bag-of-features image representation. In the proposed setup shape masks can be seen as weak geometrical constraints over bag-of-features. Those constraints can be used to reduce background clutter and help recognition. For localization, we propose a new recognition scheme based on high-dimensional hypothesis clustering. Shape masks allow to go beyond bounding boxes and determine the outline (approximate segmentation) of the object during localization. Furthermore, the method easily learns and detects possible object viewpoints and articulations, which are often well characterized by the object outline. Our experiments reveal that shape masks can improve recognition accuracy of state-of-the-art methods while returning richer recognition answers at the same time. We evaluate the proposed approach on the challenging natural-scene Graz-02 object classes dataset.