In order to model the effects of uneven spatial distribution of components and temperature a computational fluid dynamics (CFD) model has been developed for a living polymerisation reaction in a tubular reactor. The low moments of the molecular weight distribution (MWD) and the dispersity index of the product as well as the more usual spatial concentration of species and temperature have been calculated. The modelling and simulation work was carried out using the CFD code PHOENICS version 2.1 on Pentium PCs. Additionally, a novel algorithm is described which makes the design of reactor control strategies more tractable by providing a very rapid route to a qualitative approximation of the MWD of products from living polymerisation processes. Numerically simulated data generated using this new procedure are compared with slower but more rigorous approaches to the same problem. The examples cover living polymerisations in an isothermal batch reactor, a steady-state continuous stirred tank reactor (CSTR) and feed-perturbed CSTR. It is demonstrated that, although the novel algorithm comprises only four differential equations, it provides the essential information concerning the position and relative intensity of the peak(s) in a MWD plot needed for the design of reactor control strategies for the production of tailored MWDs.