A model is described which simulates icing on an unheated, non-rotating cylinder. Both rime and glaze ice can be accounted for. The model computes the thermodynamic conditions and the initial icing rate as a function of angle around the upstream face of the cylinder. Although the model is not time-dependent, the initial icing rate can be used to compute local ice thickness after a specified time interval, and these in turn allow one to plot the ice accretion profile in either a single-step or multi-step fashion. Thus it is possible to predict total ice accretion cross-sectional area and mass for ice grown under varying conditions of airspeed, air temperature and pressure, cloud liquid water content, droplet size distribution, and cylinder size. Results are presented on the stagnation line growth rate as a function of liquid water content and airspeed, and examples of accretion profiles over a range of environmental conditions are provided. Although the model may be applied quite generally, the model results presented here are applicable to aircraft icing conditions.