For the oriented solidification of molten silicon to form an ingot in a bottomless crystallization chamber (9, 41) with a cooling body (11), which can be lowered relative to the chamber, the flat bottom surface of a seed body (25) of solid silicon is laid on the surface of the cooling body. The top surface of the seed body (25) is melted, and the ingot is grown on top of it as the cooling body is lowered by relative motion with respect to the crystallization chamber (9, 41) at a rate which is dependent on the supply of additional silicon and the solidification rate. For the purpose of producing large ingots with a coarsely crystalline to monocrystalline structure, a seed body (25) with a crystalline structure selected from the group ranging from coarsely crystalline to monocrystalline is used. Either lump silicon is placed on top of the seed body (25) and melted by induction, or molten silicon is produced in a forehearth (37) and poured onto the seed body (25). The seed body (25) has a thickness of 0.3-20 mm, and preferably of 1-10 mm.