Software aging often affects the performance of a software system and eventually causes it to fail. A novel approach to handle transient software failures is called software rejuvenation which can be regarded as a preventive and proactive solution that is particularly useful for counteracting the phenomenon of software aging. In this paper, we consider the optimal software rejuvenation policy maximizing the interval reliability in the general semi-Markov framework. We derive analytically the optimal software rejuvenation timing which maximizes the limiting interval reliability or the interval reliability with exponentially distributed operation times. Further, we examine numerically the transient behavior of the interval reliability at an arbitrary operation time. Our results under the interval reliability criteria are extentions of some earlier work, since the interval reliability can be specialized to the pointwise availability and the common reliability function.