A theoretical model is proposed which describes the influence of non-uniform ionospheric conductivity distributions on ULF-pulsations. The assumption is made that the field-aligned currents carried by the wave-field are closed by polarisation currents in the magnetosphere and by the irrotational part of the ionospheric currents. Current continuity at the magnetosphere-ionosphere boundary provides for a differential equation for the reflected electric field for arbitrary non-uniform conductivity distributions. A solution of the equation for two simple but realistic conductivity and electric field distributions shows that anomalies in the reflected electric field can occur which are confined to the conductivity gradient region. Under certain conditions also double peak electric field disturbances have been obtained.