A reactivity-initiated event is a design-basis accident for the safety analysis of boiling water reactors. It is defined as a rapid transient of reactor power caused by a reactivity insertion of over $1.0 due to a postulated drop or abnormal withdrawal of the control rod from the core. Strong space-dependent feedback effects are associated with the local power increase due to control rod movement. A realistic treatment of the core status in a transient by a code with a detailed core model is recommended in evaluating this event. A three-dimensional transient code, ARIES, has been developed to meet this need. The code simulates the event with three-dimensional neutronics, coupled with multichannel thermal hydraulics, based on a nonequilibrium separated flow model. The models and verification of the code with a benchmark problem posed by the Nuclear Energy Agency Committee on Research Physics/Committee on the Safety of Nuclear Installations and by comparisons to the experimental data of tests with the SPERT III E-core are presented.