In different industrial regions, including Brazil (particularly in the oil and gas sector), onshore pipelines have become an important method of transportation and distribution of diverse products, in both liquid and gas forms. Dent or groove damage to pipelines is one of the principal causes of failure of onshore pipelines, which normally transport hazardous products that can cause harmful consequences where they are installed and along their routes. This presents both financial loss and damage to the image of the company operating the pipeline. Diverse analytic, semi-empirical methods are found in technical literature that can be used to evaluate fitness-for-purpose of an onshore pipeline with dent or groove damage. The equations suggested by these methods differ, making it doubtful which method would give the best results and should be applied. A comparative technical analysis of some of the available methods was conducted, with regard to theoretical foundation and availability and accuracy of required data to estimate failure stress. The analyzed results presented indicate the similarity of these methods, which are essentially based on classical fracture mechanics. The British gas semi-empirical method of analyzing dent or groove damage is recommended to assess pipeline fitness-for-purpose for these types of pipeline damage.