Abstract: The Dalitz plot distribution of B-0 -> (D) over bar K-0(+)pi(-) decays is studied using a data sample corresponding to 3.0 fb(-1) of pp collision data recorded by the LHCb experiment during 2011 and 2012. The data are described by an amplitude model that contains contributions from intermediate K* (892)(0), K*(1410)(0), K-2*(1430)(0) and D-2(*)(2460)(-) resonances. The model also contains components to describe broad structures, including the K-0(*)(1430)(0) and D-0(*)(2400)(-) resonances, in the K pi S-wave and the D pi S-and P-waves. The masses and widths of the D-0*(2400)(-) and D-2(*)(2460)(-) resonances are measured, as are the complex amplitudes and fit fractions for all components included in the amplitude model. The model obtained will be an integral part of a future determination of the angle gamma of the Cabibbo-Kobayashi-Maskawa quark mixing matrix using B-0 -> DK+pi(-) decays.