A model of the growth of polar stratospheric ice crystals is described, taking account of the interstitial supersaturation, the effect of radiative heat transfer, heat conduction, mass diffusion and surface kinetic processes. This last effect has commonly been neglected in treatments of solid particle growth derived from models of liquid droplet aerosols. Numerical solutions for a wide range of conditions indicate that surface kinetic effects can be the dominant rate-limiting process for small particles and low supersaturations. Outside of these conditions the surface resistance remains a significant fraction of the total resistance of growth. Limits to the application of our formula, including its application to type I particles, are outlined. ¿ American Geophysical Union 1992