Technological advancements have led to the use of computer based systems in safety critical applications. As computer based systems are being introduced in nuclear power plants, effective and efficient methods are needed to ensure dependability and compliance to high reliability requirements of systems important to safety. Even after several years of research, quantification of software reliability remains controversial and unresolved issue. Also, existing approaches have assumptions and limitations, which are not acceptable for safety applications.This paper proposes a theoretical approach combining software verification and mutation testing to quantify the software reliability in nuclear safety systems. The theoretical results obtained suggest that the software reliability depends on three factors: the test adequacy, the amount of software verification carried out and the reusability of verified code in the software. The proposed approach may help regulators in licensing computer based safety systems in nuclear reactors.