Ice maker comprising a mould (10, 110) forming at a number of mould cavities (11, 111a, 11b) for receiving water and forming a respective piece of ice (41, 42,141), which number of mould cavities are arranged in at least one column defining a longitudinal direction; a first (2, 102) and a second shaft (3, 103); an endless conveyor (100), which is arranged to convey the mould in the longitudinal direction around at least the first shaft; and drive means (8) connected to at least one of the first and second shafts for driving the conveyor. The mould (10, 110) is formed of an elastic material and arranged to be elastically deformed as the mould passes over the first shaft (2, 102). Longitudinal communication channels (13a, 113a) are arranged between consecutive mould cavities (11, 111a) arranged in one column, for allowing water to flow between mould cavities in one column. A method of fabricating pieces of ice is also disclosed.