An analytic method is presented for determining the dilation of fast reactor fuel assembly ducts. For temperatures where creep is linearly dependent on stress, the method is rigorous in satisfying equilibrium, compatibility and stress-strain equations. Solutions are presented for two cases: (1) a duct with constant pressure differential, (2) a duct with varying pressure differential. Results are in close agreement with finite element results of the MARC-CDC program. The method is used to predict the dilation of the Fast Test Reactor (FTR) ducts under different operating conditions. Presented are the stress, strain and dilation predictions along the duct wall, and the duct dilation variations with its geometric and loading parameters.