A discrete three-dimensional random walk model has been developed to s
imulate icicle growth. Water flow along the icicle's surface is divide
d into fluid elements which follow a stochastic path towards the icicl
e tip. During its motion, a fluid element may freeze on the icicle's l
ateral surface or at its tip The fluid elements may also drip from the
icicle tip. The influence of the model parameters (the freezing proba
bility, the shedding parameter and the motion parameter) on the icicle
geometry and on the efficiency of freezing has been examined. The mod
el predicts a characteristic three-dimensional icicle surface of a sto
chastic nature. This new model may be used to simulate icicle formatio
n on transmission lines, offshore structures and buildings, A distinct
advantage of the random walk model is that it is not limited by the o
bject's geometry.