The authors developed an achromatic speckle pattern interferometer able to measure in-plane displacements in polar coordinates. It has been used to measure combined stresses resulting from the superposition of mechanical loading and residual stresses. Relaxation methods have been applied to produce on the surface of the specimen a displacement field that can be used to determine the amount of combined stresses. Two relaxation methods are explored in this work: blind hole-drilling and indentation. The first one results from a blind hole drilled with a high-speed drilling unit in the area of interest. The measured displacement data is fitted in an appropriate model to quantify the stress level using an indirect approach based on a set of finite element coefficients. The second approach uses indentation, where a hard spherical tip is firmly pressed against the surface to be measured with a predetermined indentation load. A plastic flow occurs around the indentation mark producing a radial in-plane displacement field that is related to the amount of combined stresses. Also in this case, displacements are measured by the radial interferometer and used to determine the stresses by least square fitting it to a displacement field determined by calibration. Both approaches are used to quantify the amount of bending stresses and moment in eight sections of a 12 m long 200 mm diameter steel pipe submitted to a known transverse loading. Reference values of bending stresses are also determined by strain gauges. The comparison between the four results is discussed in the paper.