An integral kinetic model was used to perform a transient analysis for possible criticality accidents in different types of weakly coupled systems, showing the potential of this method for general coupled systems. A feature of the integral kinetic model is its ability to describe a time- and region-dependent fission density for a coupled system of any geometry. In this study, a fuel-solution-tank system and a fuel-debris system were analyzed. Obtained results were a fission density and a released energy in each region, and a coupling between regions. It was concluded from this study that the integral kinetic model can further be applied to other coupled systems and can provide important characteristics of the criticality accident of such systems.