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 a novel analytical approach to the interpretation of residual elastic strain measurements within slices extracted from autofrettaged tubes. The central postulate of the approach presented here is that the observed residual stress and residual elastic strains are secondary parameters, in the sense that they arise in response to the introduction of permanent inelastic strains (eigenstrains) by plastic deformation. The problem of determining the underlying distribution of eigenstrains is solved here by means of a variational procedure for optimal matching of the eigenstrain finite element model to the observed residual strains reported in the literature by Venter et al., 2000, J. Strain Anal., 35, p. 459. The eigenstrain distributions are found to be particularly simple, given by one-sided parabolas. The relationship between the measured residual strains within a thin slice to those in a complete tube is discussed.