The current–voltage characteristics of a resistive-memory structure based on non-stoichiometric tantalum oxides is numerically simulated. The results of pulsed studies of structures with different shapes of the conductive filament, such as a truncated cone with different generatrix inclination angles, are presented. It is shown how the shape and total volume of the conductive filament affects the current amplitude and the number of pulses necessary for complete filament breaking and restoration.