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Ice growth may rapidly degrade the aerodynamic performance of an aircraft. It can also severely damage structures such as communication towers or power lines. Subsequently, de-icing and anti-icing systems have been developed and a number of codes designed to predict ice shapes. When ice accretion starts, two different types of ice can appear, depending on the temperature and conditions. All of the incoming fluid may freeze almost instantaneously and turn into rime ice. Alternatively, a fraction of the incoming fluid may freeze and turn into glaze ice while the other part remains liquid and may flow over the ice. Previous work on ice accretion has mainly targeted the ice shape and neglected the owing water layer. The present study focuses on this. A set of governing equations is derived for both rime ice growth and coupled ice growth and water flow. When rime ice accretes, a mass balance is used to calculate the shape. In the presence of both ice and water, the ice growth is governed by an energy balance and the water flow by a mass balance. These equations are solved numerically for the water flow alone and the coupled ice growth and water flow for two- and three-dimensional at inclined planes. The behaviour of both ice and water is studied. The model is then extended to deal with arbitrary substrates and solutions are sought for industrially important applications such as ice accretion on power lines or aerofoils. This research work forms part of the ICECREMO project. ICECREMO is a three-dimensional ice accretion and water flow code developed collaboratively by DERA, British Aerospace, Rolls Royce, GKN Westlands Helicopters and Cranfield University under the auspices of the UK department of Trade and Industry.