Two-dimensional axisymmetrical computational models have been developed using finite element techniques to represent the rheological stiffening due to degassing-induced crystallisation and the effects of a brittle carapace within a simple lava dome. The dome is modelled numerically considering the effects of temperature, pressure and rate of extrusion. Using these state variables the bulk viscosity is derived from empirical equations and the bulk rheology approximated using a solidification viscosity, dividing the dome into solid-dominated and fluid-dominated domains. Elastoplastic equations for the solid component and fluid-mechanical equations for the fluid domain are solved simultaneously allowing continuous stress across the fluid-solid interface to ensure the two components move in unison. We apply this model, a Hookean solid carapace model and a purely fluid lava dome model to the case of the October 1980 lava dome at Mount St. Helens. The results show that dynamic growth models involving a solid carapace are required to simulate this lava dome.