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Due to a lack of modern analogues, debate surrounds the importance of tides in ancient epi-continental seas. However, numerical modelling can provide a quantitative means of investigating palaeo-tidality without recourse to analogues. Finite element modelling of the European Upper Carboniferous epi-continental seaway predicts an exceedingly low Lunar tidal range ( ca 5 cm in the open water regions of the UK and Southern North Sea). The Imperial College Ocean Model (ICOM) uses finite element methods and an unstructured tetrahedral mesh that is computationally very efficient. The accuracy and sensitivity of ICOM tidal range predictions were tested using bathymetric data from the present-day Mediterranean Sea. The Mediterranean Sea is micro-tidal and varies in depth up to 5·4 km with an average depth of 1–2 km. ICOM accurately predicts the tidal range given both a realistic, but smoothed, bathymetry and a straight sided basin with a uniform depth of 1 km. Variation in uniform depth from 100 to 3000 m with and without islands consistently predicts micro-tidality, demonstrating that the model is robust and the effect of bathymetric uncertainty on model output is relatively small. The extremely low tidal range predicted for the European Upper Carboniferous is thus deemed robust. Putative Upper Carboniferous tidal deposits have been described in the UK and southern North Sea, but are represented by cyclic rhythmites and are limited to palaeo-estuaries. Calculations based on an embayed coast model show that the tidal range could have been amplified to ca 1 m in estuaries and that this is sufficient to form cyclic rhythmites. Without tidal mixing, the tropical equatorial heat and salinity enhancement would promote stratification in the open water body. The introduction of organic matter probably caused anoxia, biotic mortality and carbon accumulation, as evidenced by numerous black ‘marine-band’ shales. [ABSTRACT FROM AUTHOR]