A stochastic corrosion growth model is established for underground pipeline structures. The model has been developed with the concept in mind that the evolution of localized corrosion damage is time-dependent following an activation stage (nucleation) - growth stage (propagation) - steady state stage (passivation) mechanism. The temporal correlation of the defect evolution is able to be well represented by a geometric Brownian bridge process. The variation of activation time is taken into consideration. Two applications are illustrated: 1) predicting the evolution of the probability density function (PDF) of the corrosion depth, and 2) assessing the reliability of a pipeline structure. (C) 2019 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.