This work introduces two different approaches to explain the growth of silicon carbide (SiC) filaments, found in the bulk material and in grain boundaries of solar cells made from multicrystalline (mc) silicon. These filaments are responsible for ohmic shunts. The first model proposes that the SiC filaments grow at the solid-liquid interface of the mc-Si ingot, whereas the second model proposes a growth due to solid state diffusion of carbon atoms in the solid fraction of the ingot during the block-casting process. The melt interface model can explain quantitatively the observed morphologies, diameters and mean distances of SiC filaments. The modeling of the temperature- and time-dependent carbon diffusion to a grain boundary in the cooling ingot shows that solid state diffusion based on literature data is not sufficient to transport the required amount of approximately 3.4 1017 carbon atoms per cm2 to form typical SiC filaments found in grain boundaries of mc-Si for solar cells. However, possible mechanisms are discussed to explain an enhanced diffusion of carbon to the grain boundaries.