This paper reports on the elemental geochemistry of 47 shale samples from the uppermost Hirnantian–lowermost Rhuddanian Tanezzuft Formation, collected from drill core (depth interval 20.8–73.2 m) from borehole JA-2 at the eastern Kufra Basin, SE Libya. Eighteen of these samples were also analysed by X-ray diffraction. This study was carried out (i) to search for shales with high total organic carbon (TOC >3 wt%) and associated high uranium (U > 30 ppm) concentrations, commonly referred to as ‘hot’ shales, (ii) to test whether TOC and U correlate, (iii) to study the effects of surface weathering on the behaviour and mobility of major oxides, trace elements and rare earth elements (REE), and (iv) to examine the relationship of the elemental composition obtained in this study and Rock-Eval pyrolysis and kerogen data obtained in previous studies on the same core samples. The studied core can be divided into three intervals: upper weathered section (20.8–46.5 m, influenced by Quaternary weathering), unweathered section (46.5–68.5 m), and lower weathered section (68.5–73.9 m, influenced by latest Ordovician weathering). Overall, the shales have low TOC values (<1 wt%) and low U concentrations (<12 ppm). TOC and U do not show any correlation likely due to their low values. Hence, ‘hot’ shale has not yet been proven in this part of the Kufra Basin. Trace elements such as Mn and Sc show significant changes from the weathered into the unweathered core section. In contrast, the majority of the major oxides, trace elements and REE seem to be unaffected or at least largely unaffected by weathering processes. The exception is the transition from the unweathered section into the lower weathered section of the core. Here, most of the major oxides, trace elements and REE show either abrupt or gradual shifts towards lower or higher element concentrations. The observed whole-rock geochemical (e.g., K2O, Rb, Sr, Th/K) and mineralogical (e.g., kaolinite/illite, K-feldspar/quartz) changes suggest either a switch from one source area to another or, more likely, climatic influence. The deepest part of the core may have been influenced by a more humid and warm climate that has led to intensive chemical weathering and dissolution of K-feldspar. During the latest Hirnantian–earliest Rhuddanian a temporary emersion event may have occurred due to post-glacial rebound, which has led to the weathering of older strata.