For most of the destructive methods used for measuring residual stresses, the relationship between the measured deformations and the residual stresses are in the form of an integral equation, typically a Volterra equation of the first kind. Such equations require an inverse method to evaluate the residual stress solution. This paper demonstrates the mathematical commonality of physically different measurement types, and proposes a generic residual stress solution approach. The unit pulse solution method that is presented is conceptually straightforward and has direct physical interpretations. It uses the same basis functions as the hole-drilling integral method, and also permits enforcement of equilibrium constraints. In addition, Tikhonov regularization is shown to be an effective way to reduce the influences of measurement noise. The method is successfully demonstrated using data from slitting (crack compliance) measurements, and excellent correspondence with independently determined residual stresses is achieved.