The random cluster model on a planar graph can be reformulated as a loop model on the corresponding medial graph. For a configuration ω ω of the random cluster model, the corresponding loop configuration is the set of self-avoiding loops that separate the clusters from the dual clusters. In the transfer matrix approach, the loop model is written in terms of a Temperley-Lieb algebra with the parameter δ δ = q . In two dimensions, the random cluster model is therefore closely related to the O(n) model, which is also a loop model.