Research on the incorporation of compressibility effects, for both the liquid and radiolytic gas phases, into the Finite Element Transient Criticality (FETCH) coupled neutronics/computational fluid dynamics code is described. The code has been developed to simulate criticality transients in multiphase media and is applied here to fissile solution transient criticality. The predicted fission and pressure transients obtained by the enhanced numerical model are benchmarked against the results from the SILENE series of experiments on criticality transients in uranium solutions. The amplitude and the form of the first pressure peak, following a step reactivity change, are well represented, and insight is gained into the form of subsequent pressure oscillations. An explanation is given on the absence of these oscillations in more energetic transients.