Through theoretical analysis, Chen and Lamb [1994] showed that the shape of an ice crystal due to depositional growth is controlled by two main factors: 1) the difference in the condensation coefficients of the prism and basal faces of the ice crystal, which is primarily a function of temperature, and 2) the difference in fluxes of water vapor to the prism and basal faces of the crystal. The vapor density gradients around a non-spherical particle and ventilation effects were also considered. Based on this theoretical analysis, a simple parameterization of the shape of an ice crystal grown by vapor deposition was developed that agreed well with previous empirical relations derived from observational data, providing a physical explanation for the observed form of the power law. The exponent of the power law turns out to be identical to the inherent growth rate (the ratio of the basal-face and prism-face condensation coefficients). This scheme was used to simulate the growth of ice crystals under both fixed and time varying conditions, with good agreement with previous results. This parameterization scheme developed on theoretical grounds provides a self-consistent way for understanding the evolution of ice crystal sizes and shapes, and may lead to improved microphysical parameterizations of ice crystal growth and shape in cloud and mesoscale models.