We will discuss the reliability analysis of the constant stress accelerated life tests when a parameter in the generalized gamma lifetime distribution is linear in the stress level. Statistical inference on the estimation of the underlying model parameters as well as the mean time to failure and the reliability function will be addressed on the basis of the maximum likelihood approach. Large sample theory will be derived for the goodness of fit of the data. Some simulation study and an illustrative real example will be presented to show the appropriateness of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.