Constitutive equations obtained from the creep behaviour of 99.9 wt % pure Bi and from Sn-10wt% Bi single-phase solid solution are applied in the continuum mechanics creep model of Tanaka et al. [1] to predict the creep behaviour of a eutectic Bi-42 wt % Sn alloy. At low stresses, Bi is the load bearing phase, while at high stresses, Sn-10 wt % Bi is the load bearing phase. The continuum mechanics creep model is able to predict the shape of the steady-state versus strain curves. However, the model predicts creep rates that are generally lower than the data. This inconsistency may be caused by a phase boundary sliding contribution to the creep rate, which is unaccounted for by the model. Creep tests done on Sn-42wt% Bi samples having various microstructural morphologies support this conclusion, where the more spheroidized microstructure creeps faster.