Most of the previous work on optimal design of accelerated life test (ALT) plans has assumed instantaneous changes in stress levels, which may not be possible or desirable in practice, because of the limited capability of test equipment, possible stress shocks or the presence of undesirable failure modes. We consider the case in which stress levels are changed at a finite rate, and develop two types of ALT plan under the assumptions of exponential lifetimes of test units and type I censoring. One type of plan is the modified step-stress ALT plan, and the other type is the modified constant-stress ALT plan. These two plans are compared in terms of the asymptotic variance of the maximum likelihood estimator of the log mean lifetime for the use condition (i.e. avar\[ln (0)]). Computational results indicate that, for both types of plan, avar\[ln (0)] is not sensitive to the stress-increasing rate R, if R is greater than or equal to 10, say, in the standardized scale. This implies that the proposed stress loading method can be used effectively with little loss in statistical efficiency. In terms of avar\[ln (0)], the modified step-stress ALT generally performs better than the modified constant-stress ALT, unless R or the probability of failure until the censoring time under a certain stress-increasing rate is small. We also compare the progressive-stress ALT plan with the above two modified ALT plans in terms of avar\[ln (0)], using the optimal stress-increasing rate R* determined for the progressivestress ALT plan. We find that the proposed ALTs perform better than the progressivestress ALT for the parameter values considered.