The dynamics of the molten salt reactor (MSR), one of the Generation IV International Forum concepts, was studied. The graphite-moderated channel-type MSR was selected for numerical simulation. MSR, a liquid-fueled reactor, has specific dynamics with two physical peculiarities: The delayed neutron precursors are drifted by the fuel flow, and the fission energy is released directly into the coolant. Presently, there are few accessible numerical codes appropriate for MSR simulation; therefore, the DYN1D-MSR and DYN3D-MSR codes were developed based on the light water reactor dynamics code DYN3D. These allow calculation of one-dimensional and full three-dimensional transient neutronics in combination with parallel channel-type thermal hydraulics. The codes were validated with experimental results of the Molten Salt Reactor Experiment from Oak Ridge National Laboratory and applied to several transients typical for a liquid fuel system. Those transients were initiated by reactivity insertion, by cold or overfueled slugs, by the fuel pump start-up or shutdown, or by the blockage of selected fuel channels. In these considered transients, the response of MSR is characterized by the immediate change of the fuel temperature relative to the temperature at that power level. This causes fast insertion of feedback reactivity, which is negative for power-related temperature increase. On the other hand, the graphite response is slower, and its feedback coefficient depends on the core size and geometry. The addition of erbium to the graphite can ensure negative feedback and inherent safety features also for big low leakage cores. The DYN1D-MSR and DYN3D-MSR codes have been shown to be effective tools for MSR dynamics studies. The MSR response to the majority of transients is considered acceptable within safety margins as long as the graphite feedback coefficient is negative. A transient that is possibly an exception is a local channel blockage.