Detailed mapping of topography is crucial for the understanding of processes shaping the surfaces of planetary bodies. In particular, stereoscopic imagery makes a major contribution to topographic mapping and especially supports the geologic characterization of planetary surfaces. Image data provide the basis for extensive studies of the surface structure and morphology on local, regional and global scales using photogeologic information from images, the topographic information from stereo-derived digital terrain models and co-registered spectral terrain information from color images. The objective of the Psyche topography and geomorphology investigation is to derive the detailed shape of (16) Psyche to generate orthorectified image mosaics, which are needed to study the asteroids’ landforms, interior structure, and the processes that have modified the surface over geologic time. In this paper we describe our approaches for producing shape models, and our plans for acquiring requested image data to quantify the expected accuracy of the results. Multi-angle images obtained by Psyche’s camera will be used to create topographic models with about 15 m/pixel horizontal resolution and better than 10 m height accuracy on a global scale. This is slightly better as global imaging obtained during the Dawn mission, however, both missions yield resolutions of a few m/pixel locally. Two different techniques, stereophotogrammetry and stereophotoclinometry, are used to model the shape; these models will be merged with the gravity fields obtained by the Psyche spacecraft to produce geodetically controlled topographic models. The resulting digital topography models, together with the gravity data, will reveal the tectonic, volcanic, impact, and gradational history of Psyche, and enable co-registration of data sets to determine Psyche’s geologic history.