The development of Spin-Transfer Torque Magnetic RAMs (STT-MRAMs) mass production requires high-quality test solutions. Accurate and appropriate fault modeling is crucial for the realization of such solutions. This paper targets fault modeling and test generation for all interconnect and contact defects in STT-MRAMs and shows that using the defect injection and circuit simulation for fault modeling without incorporating the impact of magnetic coupling will result in an incomplete set of fault models; hence, not obtaining accurate fault models. Magnetic coupling introduced by the stray field is an inherent property of STT-MRAMs and may foster the occurrence of additional memory faults. Not considering the magnetic coupling clearly will give rise to test escapes. The paper introduces a compact model for STT-MRAM that incorporates the intra- and inter-cell stray field, uses this model to derive the full set of fault models for interconnect and contact defects, and finally proposes an efficient test solution.