In this paper, we summarize some recent results, in which the process of creep crack growth is modelled using time-dependent finite element methods. For stationary cracks, the time-dependent stress-strain field around the crack tip region can be accurately determined. We then proceed to a study of crack propagation. To achieve this a general damage model is developed based on two parameters — a critical effective strain for material failure, and a characteristic propagation distance. The model is used to study crack propagation in 2 1/4 Cr-1 Mo steel. The crack growth rates obtained from these numerical studies agree well with available experimental data for the same material. The correlation of creep crack growth data under non-steady stress fields is also discussed. The results have significant implications for the assessment of structural integrity.