Wire arc additive manufacturing (WAAM) is an advanced metal 3D printing technique that has great prospects in structural engineering for its ability to produce large and intricate components. Residual stresses arising from the complex thermal history of the WAAM process can significantly affect the structural performance of manufactured components, such as fatigue life, part distortion and the load-bearing capacity. This study experimentally investigates the residual stress distributions in square hollow section (SHS) and circular hollow section (CHS) tubular elements manufactured via WAAM. A total of five WAAM steel specimens were produced using ER 90S-6 welding wire, including three SHS tubes with nominal thicknesses of 3.5 mm, 4.5 mm and 5.5 mm, and two 3.5 mm-thick CHS tubes with interpass temperatures of 150°C and 350°C. The sectioning method was employed to measure the residual stresses in the specimens. A detailed analysis of the residual stress patterns along the longitudinal and transverse directions was conducted, and the effects of geometric parameters and interpass temperatures were investigated. It was revealed that in the CHS tubes, higher interpass temperatures resulted in lower bending residual stresses in the longitudinal direction, while the membrane residual stresses remained effectively zero across the circumference. For the SHS tubes, in the longitudinal direction, tensile residual stresses were mainly present at the corners with a maximum value of 0.5fy (fy is the yield strength) and compressive stresses in the middle of the faces with a maximum value of -0.3fy, while in the transverse direction, the lower and upper parts of the tubes experienced the highest tensile residual stresses approximately equal to 0.35fy. The residual stress patterns were shown to be similar for SHS tubes with different thicknesses. These results provide critical insights into the residual stress distribution in WAAM tubular parts, contributing to the understanding of the structural performance of additively manufactured components.