In the design of tubular bridges, engineers have found the fatigue performance of the joints to be a critical aspect that may have a significant impact on the economic viability of these structures. In looking for ways of improving this performance, the use of residual stress-based post-weld treatment methods has been suggested. To study this possibility, preliminary laboratory tests were carried out at ICOM, which demonstrated the merits of these methods vis-à-vis their ability to increase the fatigue lives of tubular bridge joints. Although encouraging, a number of concerns with the use of these methods have limited the extent to which findings such as these can be translated into practical guidelines. Firstly, there is some concern in general about the reliability of these methods under realistic, variable amplitude loading conditions. Secondly, in the ICOM tests, it was seen that the benefit of concentrated treatment of the critical crack site, although substantial, was limited by cracking at a less critical, untreated site. On this basis, further analytical study of the post-weld treatment of tubular bridge structures was deemed necessary. Towards this end, the work presented in the current thesis was undertaken with the following main objectives: to develop models for predicting the fatigue behaviour of single (untreated or treated) crack sites and tubular structures with multiple potential crack sites using a probabilistic approach, to predict, using these models, the potential benefit of treating tubular bridge structures, and to assess the suitability of post-weld treatment methods for tubular bridge applications, in view of the results of the work carried out to meet the other thesis objectives. In the first chapters of the thesis, the steps involved in the development of the various models are described. The probabilistic model developed to predict the fatigue behaviour of single crack sites is based on a deterministic linear elastic fracture mechanics (LEFM) model. The model developed to analyze tubular structures with multiple potential crack sites employs a systems reliability approach. Specifically, the tubular structure is represented as a series system with an unknown level of correlation between the system elements. With the resulting models, parametric studies are carried out using the example of a typical highway bridge to determine the effects of treatment intensity, quality (i.e. uniformity), coverage, timing, and depth on the benefit of post-weld treatment. A number of complementary studies are then conducted to address specific concerns not addressed elsewhere. Based on this work, the following conclusions are highlighted: Using the developed probabilistic models, it is shown that significant improvements in fatigue performance can be obtained through the post-weld treatment of tubular bridge structures. For full-scale bridge structures under realistic loading conditions, the benefit of treatment is more sensitive to the treatment intensity than the treatment quality or depth. Based on the comparison of the various levels of treatment coverage, a partial treatment strategy is proposed, which is seen to be just as effective as a strategy of full treatment. Of all the parameters varied in the parametric studies, the effect of treatment timing is seen to be the most significant. Specifically, it is observed that a significant increase in the benefit of treatment can be realized if the treatment is applied in the field as opposed to the shop. A preliminary economic study of needle peening in the shop demonstrates that the economic benefits of this approach may be limited or even non-existent in some cases, but significant in others. More promising results are obtained in a similar study for field treatment.