Reliable evaluation of residual stress (RS) is essential in structural integrity assessment for critical components such as welded joints. Being able to provide a 2D cross-sectional stress map over a cutting plane, the contour method (CM) is often used for assessing butt-welds and other components with rectangular cross-sections. For components such as T-sections, sacrificial material is often employed to render a rectangular cutting path to prevent cutting artefacts. This is because artificial stresses can appear in back-calculated results when there are sudden changes in cutting length during wire electro discharge machining (WEDM). Sacrificial material can be used to compensate, but this may be impractical for large or irregular components, where a perfect match between sacrificial material and the original component cannot be easily achieved. We demonstrate a new technique for CM analysis employing a stress-free sample, realised on welded Ti-6Al-4V T-sections to evaluate cutting artefacts (CAs) and the proposed correction method. It will be shown that back calculated stress calculated based on stress-free samples can be considered as artificial stresses introduced during WEDM process. A correction on a conventional CM analysis has been achieved by subtracting these artificial stresses from original CM results. The total artificial stress introduced by cutting a variable cross-section component will be presented, along with a discussion on this effect on quantifying stresses at weld roots employing the CM. It has been found that this technique is capable of mitigating cutting artefacts, especially when applied to components with complicated profile where changes in cutting length exist.