The Dalitz plot distribution of $B^0 rightarrow bar{D}^0 K^+ pi^-$ decays is studied using a data sample corresponding to $3.0rm{fb}^{-1}$ 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 $Kpi$ S-wave and the $Dpi$ 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 CKM quark mixing matrix using $B^0 rightarrow D K^+ pi^-$ decays.
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