Incremental Hole Drilling is a well-established technique for measuring residual stresses; it involves relaxing residual stresses by incrementally drilling into the material and simultaneously measuring strains using strain gauge rosettes. The measured strains and residual stresses are related by an integral formulation, so an elastic inverse solution is required to calculate the stress field. Typically, strains are measured at different depths than those at which the residual stress calculation is performed. Therefore, it is common practice to fit the strain measurements at depth using polynomials or splines. However, the choice of fitting parameters can critically affect the final measurement output. This study evaluates the uncertainty associated with the deformation fitting procedure using Gaussian Process Regression, a probabilistic machine learning algorithm capable of producing uncertainties associated with the fit itself. These fit uncertainties were then propagated to the residual stresses through a Monte Carlo simulation. The developed methodology was applied to AA 7050-T7451 aluminum samples surface treated by laser shock peening.