Circumferential upstream propagation of a premixed flame in a region confined between two concentric tubes is considered. The cold flow in this configuration features rotational motion and the flame is modelled as an interface separating the burned and unburned gases. Through an analytical solution of the integral form of the governing equations, it is shown that the static pressure increases across the flame. Hence, the circumferential propagation of the flame is associated with the generation of an adverse pressure gradient. The theoretical prediction of the pressure increase is, further, supported by the experimental observations and discussed in the context of the theory of flame back pressure. The results extend the recent findings on the generation of adverse pressure gradient during the axial propagation of swirling flames, to the circumferential direction. It is argued that the demonstrated pressure gain across the flame can significantly facilitate flame flashback.