The neutron kinetic analysis methods for the molten-salt reactors are quite different from those for conventional solid-fuel reactors, which do not take into account the flowing-fuel-induced neutronics effects. Therefore, for dynamics and safety analyses of the molten-salt reactor systems, the conventional kinetics codes would not be appropriate to accurately predict its transient behaviors. A point-kinetics with flowing- fuel model has been used to assess the fluid-fuel reactor system safety, but recognized as not to be sufficient to simulate spatial distributions of delayed-neutron precursors and neutron populations during transients for given detail reactor models. In order to meet this requirement, AMBIKIND, a 2-group, 2-dimensional neutron kinetics code suitable for the molten-salt reactor systems was developed. This paper explains the code's theoretical and numerical descriptions and, as a part of its verification, includes some simulation results of MSRE stability experiments. Even though the present reactor model does not include the recirculation effect of the fuel-salt through the reactor system, the AMBIKIN2D code should be able to predict the power and phase shift at various power levels and reactivity insertions with better accuracy.