New bivariate models for soot particle structure are introduced to qualitatively replicate observed particle shapes and are found to offer quantitative improvements over older single-variable models. Models for the development of particle shape during surface growth and for particle collision diameters are described and implemented along with two models taken from other published work. Using a stochastic approach, bivariate soot particle distributions are calculated for the first time. Distributions calculated for the new models are found to be insensitive to the collision diameter model used for coagulation. The total mass of soot produced in a laminar premixed flame is found to vary by no more than 20% as the model for the geometric effects of chemical reactions on the surface of particles is changed. Histories of individual particles are analyzed and show the limitations of collector particle techniques for predicting the evolution of aggregate shape descriptors. (c) 2007 The Combustion Institute. Published by Elsevier Inc. All rights reserved.