This work in the area of modeling of natural phenomena in computer graphics presents a new, physically based model for the natural process of icicle growth and implements the model creating photorealistic icicle images at the various stages of their growth. The physical model developed here is based on the analysis of the mechanical and thermodynamical processes involved (surface tension, contact angle and wetting, heat transfer, and thermal conductivity). The model is simulated by discrete simulation, yielding an icicle-surface description. This description is converted to Bezier patches and then raytraced.