This paper presents a theory for the prediction of pressures in circular silos under concentric mixed flow, assuming an internal flow channel of conical profile with straight but inclined sides. The theory is based on a generalised application of the classical method of ‘slice equilibrium’ together with additional assumptions based on a treatment of the granular solid as a Coulombic material. Only one of the resulting pair of coupled linear ordinary differential equations may be solved in closed form, while both numerical and approximate closed-form solutions are explored for the other. The derivation of the theory is presented in full and a series of parametric studies explores the predictions and compares these with qualitative observations from experiments. In particular, the significant overpressure that is known to occur at the ‘effective transition’, where the internal flow channel intersects with the silo wall, may be estimated quantitatively for the first time.