Icing has been identified as a major hazard for aviation safety since the beginning of aeronautical engineering. This paper is focused on ice crystal icing (ICI) which is related to ice accretion for an aircraft in flight in the presence of ice particles. Liquid water is necessary for the ice crystals to stick to the walls of the internal components of an aircraft engine. Emphasis is put on the glaciated conditions where the required liquid water comes from the melting of the ice crystals themselves when they enter a warm environment (the engine core). ICI represents an important concern for flight safety in addition to classical supercooled water icing where the accreted ice only derives from the instantaneous freezing of supercooled liquid droplets when they hit an obstacle. A semi-empirical model which accounts for the influence of the ice crystals on the mass and momentum balance equations is proposed. It accounts for the liquid transport in the porous ice layer and for the ice crystal sticking efficiency. The physics is extremely complicated and not completely understood. Therefore, several adjustable parameters are used in the model. However, the model predictions agree well with the existing experimental data. In particular, the model is able to predict typical conical accretion shapes that are never found in classical supercooled water icing conditions. Moreover, the influence of the ice crystal melting ratio on the accretion shapes is properly accounted for. (C) 2018 Elsevier Ltd. All rights reserved.