Existing engineering methods to ensure fracture propagation control in natural-gas transmission pipelines have been shown to be non-applicable when dense-phase CO2 is transported. To overcome this, a coupled fluid–structure interaction model has been developed. It consists of a homogeneous equilibrium flow model, coupled with the Span–Wagner equation of state and including solid-phase formation, and a finite-element model of the pipe taking into account large deformations and fracture propagation through a local fracture criterion.Model predictions are compared with data from two medium-scale crack-arrest experiments with dense-phase CO2. Good agreement is observed in fracture length, fracture-propagation velocity and pressure. Simulations show that, compared to natural-gas pipelines, the pressure level at the opening fracture flaps is sustained at a much higher level and at a much longer distance behind the moving fracture tip. This may be one important reason why the existing engineering methods do not work for dense-phase CO2.