The contour method is one of the promising techniques for the measurement of residual stresses in engineering components. In this method, the cut surfaces deform, owing to the relaxation of residual stresses. The deformations of the two cut surfaces are then measured and used to back calculate the 2-dimensional map of original residual stresses normal to the plane of the cut. Thus, it involves four main steps; specimen cutting, surface contour measurement, data analysis and finite element simulation. These steps should perform in a manner that they do not change the underlying features of surface deformation especially where the residual stress distribution varies over short distances. Therefore, to carefully implement these steps, it is important to select appropriate parameters such as surface deformation measurement spacing, data smoothing parameters (‘knot spacing’ for example cubic spline smoothing) and finite element mesh size. This research covers an investigation of these important parameters. A simple approach for choosing initial parameters is developed based on an idealised cosine displacement function (giving a self-equilibrated one-dimensional residual stress profile). In this research, guidelines are proposed to help the measurer to select the most suitable choice of these parameters based on the estimated wavelength of the residual stress field.