Software verification and validation constitute crucial phases in the development of simulation computer codes, particularly in the context of nuclear reactor safety analysis codes, where stringent safety requirements govern the development and deployment of nuclear technologies. This paper focuses on numerical verification study of the System Analysis Module (SAM) computer code, currently under development at Argonne National Laboratory. Specifically, we employed the Method of Manufactured Solutions (MMS) and proposed a verification technique tailored to the multiphysics simulation of molten salt reactors (MSRs). This research accomplished three main objectives. First, we have addressed key challenges associated with applying the MMS to MSR systems, arising from (1) the complex multiphysics coupling inherent in this problem and (2) the necessity to model the entire coolant loop for describing the drift of delayed neutron precursors outside the reactor core. The paper provides recommendations and guidelines to overcome these challenges, enabling the successful application of the MMS for simulating MSRs. Second, we have presented a comprehensive set of verification examples, serving as an exhaustive benchmark for code verification within the nuclear community. Third, we have established a robust verification of the SAM code’s capability to model MSR systems.