In this presentation we discuss the efficient preconditioning of a discretized multiphase flow system that arises in the finite element solution of a continuum model that has been proposed for vascular tumour growth. The model considers four incompressible viscous fluid phases, representing healthy cells, tumour cells, blood vessels and extracellular material respectively. Equations are derived for mass balance, momentum balance and the transport and consumption of nutrients. Time-dependent simulations undertaken in two and three space dimensions demonstrate that solution of the discretized momentum system is by far the most time-consuming component of each time step: hence this is the primary focus of the talk. This multiphase momentum system will be described in detail, along with its discretization using Firedrake. The ordering of the unknowns is selected to allow an efficient block preconditioner to be developed, based upon Schur complement with algebraic multigrid blocks, which is implemented and tested using the “field split” capability provided by PETSc. Results will be presented for sequences of increasingly fine unstructured meshes in 2D (triangles) and 3D (tetrahedra), using up to 168 parallel cores. Both the optimality and the parallel performance of the preconditioner will then be discussed. The main significance of this work is to allow high resolution, 3D simulations to be undertaken using this tumour-growth model over extended periods of time. Without nearoptimal preconditioning this would be prohibitively expensive.