A simple method for estimating residual stresses using the GLOSS analysis is presented, and a shakedown assessment method is proposed. Practical pressure components exhibit some local elastic follow-up, and thereby induce smaller residual stresses than implied by uniaxial models. In this context, the effectiveness of “autofrettaging” is examined by studying a thick-walled cylinder subjected to an internal pressure. Modifications to the P + Q stress-intensity limit are suggested, and compared with Roche’s criterion. The method presented here is useful for configurations experiencing small to medium amounts of follow-up, which covers many practical situations.