Autofrettage is a treatment process that uses plastic deformation to create a state of permanent residual stress within thick-walled tubes by pressurizing them beyond the elastic limit. The present paper presents explicit analytical formulas for residual elastic strains within the tube wall derived on the basis of the classical elastic–ideally plastic solution. Then the problem is addressed of rational interpretation of the radial and hoop residual elastic strains measured at a fixed number of points. To this end, the mismatch between the experimental measurements and theoretical predictions of the residual elastic strains is represented in the form of quadratic functional, , the minimum of which is sought in terms of the problem parameters, namely, the material yield stress, , and the radial position of the elastic-plastic boundary, . It is shown that shows an approximately parabolic variation in terms of either parameter when the other is fixed, and that therefore the global minimum of can be readily found. This procedure is implemented and applied to a set of experimental data on neutron diffraction measurements (Venter, A.M., de Swardt, R.R., and Kyriacou, S.,2000, J. Strain Anal., 35, pp. 459–469). In conclusion, further applications of this family of interpretation approaches are discussed.