As pipelines age, a flaw population that varies initially along the pipeline can advance in size and number. Analysis of the serviceability of pipelines based on either inline inspection or hydrotesting can lead to overly conservative decisions or an excessive risk of failure when the random nature of this population and the pipeline’s properties are represented by a “typical” flaw and “average” properties. It follows that decisions on serviceability should reflect the random nature of the variables involved or be justified by demonstrating that the uncertainty in these parameters does not adversely affect cost and safety. This is the first in series of two papers generated from a recent study on risk-based analysis for developing strategies to ensure pipeline integrity. In this paper (Part I—Theory), a new probabilistic methodology is developed to conduct fracture evaluations of pipelines subjected to ductile flaw growth in service. The study is made under the assumption that continuing serviceability is based on the use of hydrotesting. The analysis involves time-dependent elastic-plastic fracture mechanics for the underlying deterministic model, and Monte Carlo simulation for structural reliability analysis. Using these models, pipe fracture evaluations will be conducted in the light of a hydrotest-based approach to ensure pipeline integrity. They will be discussed in the companion paper, Part II—Applications (Rahman and Leis, 1994).