A new approach to the problem of optimal software testing time is described. Most models implicitly assume the testing is terminated at the end of a prescribed period of time without user's approval. It means the release time and the in-service reliability are determined unilaterally by the developer. If software developer uses and maintains it, the assumption is appropriate. But, it may be inappropriate, if a software requiring more stringent reliability is developed by second party on a contract basis. In this case, the time of release is usually determined with the user's approval. To overcome the weaknesses of the assumption, a two stage testing with failure-free release policy is proposed. A software, after being tested by the developer for some time (in-house testing), is transferred to acceptance testing performed jointly with the user. During the acceptance testing, it is released when τ units of time specified by user is observed to be failure-free for the first time. The policy may be attractive to a user because he can determine the time of release, and extend the testing time by increasing τ. A software cost model for the policy is developed. For the software developer, an optimal in-house testing time minimizing software cost, and various quantities of interests, such as expected periods of acceptance testing, are derived based on the Jelinski-Moranda software reliability model. Finally, numerical examples are shown to illustrate the results.