AbstractA mathematical/computational model for the approximate prediction of ice accretion on a conductor of finite torsional stiffness is constructed. The model, which is adapted to allow for the attachment of counterweights along the span, is three‐dimensional and time‐dependent. In the absence of counterweights, axial growth is predicted near the anchors, and cylindrical‐sleeve growth at the centre of the conductor span. The latter is caused by eccentric ice loading on the windward side of the conductor which then induces the conductor to rotate.The ‘icing‐clock’ model, based on the use of the large relaxation time approximation for particle impaction, yields an upper bound to the mass of ice accreted. At the end of each deposit time the torque density along the conductor span due to ice loading is calculated. On solving the non‐linear torsion equation for the conductor the rotation of the conductor and location of the evolving ice surface as a function of the distance from the tower and the accretion time are then deduced.Numerical results are given for conductor with varying mechanical properties, which are represented in terms of a single dimensionless torque parameter, with and without the attachment of counterweights. For a specific case illustrative results are given for the mass of ice accreted and conductor rotation when one, two, three and four counterweights are attached per span.