The critical heat flux (CHF) of flow boiling heat transfer in the vertical downward flow of a highly viscous fluid has been investigated for a consistency index eta0 = 1.49-20.88 Pa s(n), a tube diameter D = 5.34, 7.71 and 10.27 mm, a mass velocity G = 4.57-53.4 kg m-2 s-1, an inlet quality X(IN) = -1.3% to 20% and a critical heat flux q(C) = 20.1-69.2 kW m-2. A correlation based on the CHF data has been developed which takes account of the effects of Re, Pr, Bo, 1/D and P(R) on CHF.