The Tertiary palaeodrainage system in the Namibian calcrete-uranium province is deeply buried under Cenozoic sediments (such as fluvial, alluvial and desert flash-flood terrace sediments, duricrusts and/or aeolian and fluvially reworked aeolian sands) and has no obvious surface expression, because of which, this province remains under-explored in spite of hosting the world's largest calcrete-uranium deposit at Langer Heinrich. This paper presents first-pass bedrock geology and bedrock topography models for the Namibian calcrete-uranium province generated using air-borne magnetic data, which are further used to delineate subsurface Tertiary palaeochannels in the province. Conjunctive interpretations of surface geology, bedrock geology, and bedrock topography indicated that the major underlying controls on the spatial distribution and configuration of the Tertiary palaeochannels in the Namibian province are both lithological and structural; however, the basement structural fabric that formed during the Damaran orogeny possibly exerts a fundamental control on both palaeodrainage as well as present drainage. The analysis also indicated that the carnotite deposition in the Langer Heinrich palaeochannel is possibly a consequence of westward reorientation of the course of the proto-Swakop river. Finally, the paper presents a manual prospectivity analysis of the province for calcrete-uranium deposits, which resulted in the demarcation of five prospective sections of palaeochannels in the Tumas Basin, Swakop River and Khan River terraces and in the Gawib Flats (west of the Langer Heinrich Deposit).