Numerical modeling of criticality transients in dilute plutonium solutions is presented. The solutions concerned may be expected to have an overall positive temperature coefficient of reactivity at ambient temperatures. Simulations were performed using the FETCH coupled radiation transport-multiphase hydrodynamics code for the cases of step and ramp reactivity insertions. The code has been developed for modeling scenarios beyond the reach of experiment and has been extended to cover the coupling of radiolytic gas behavior and pressure. It is demonstrated that dilute plutonium criticality excursions may be terminated by radiolytic gas evolution provided that the gas is allowed to evolve freely, and that this may result in modest fission yields. However, it is also demonstrated that suppression of radiolytic gas bubbles by pressure may give rise to considerably energetic excursions with consequent large yields.