A new method for the characterisation of receiving mutual impedances of compact arrays with omni-directional antenna elements is proposed. Based on a large number of incident waves coming from different directions, the new method is able to calculate the receiving mutual impedances of omni-directional antennas based on a system of equations that characterise the received terminal voltages at different incident wave directions. In the new method, the receiving mutual impedances of all the antenna elements are calculated together in a single equation with the scattering effect from all antenna elements in the array being taken into account. Compared to the previous methods for the characterisation of the receiving mutual impedances, the new method preserves the boundary conditions of the original electromagnetic problem and produces much more accurate results on receiving mutual impedances, especially for compact antenna arrays. Direction finding examples based on the new method demonstrate its superior performance over existing methods.