AbstractIn this paper the formation and structure of an atmospheric undular bore is examined with the aid of a numerical model and theoretical analysis. the numerical model is first used to simulate a density current propagating into an unstratified environment. A detailed comparison of the model results with existing theory shows that for a given pressure head the current can travel at a greater speed than that predicted by irrotational theory.When the density current is allowed to propagate into a low‐level stable layer it is found that for certain parameter regimes an undular bore forms ahead of the current. the results for two different types of stable layers are examined. For a layer with a step profile of potential temperature, comparison is made with both classical bore theory and the theory of density currents in two‐layer fluids and encouraging agreement is found. When a linear profile is specified in the stable layer it is found that energy‐conserving solutions can be obtained. the numerical fields are then compared with measurements of the morning glory, an undular bore observed in north‐eastern Australia, and again agreement is good.Finally, preliminary results of model simulations with stratification above the stable layer are di