Spin-transfer-torque magnetic RAM (STT-MRAM) is one of the most promising emerging memory technologies. As various manufacturing vendors make significant efforts to push it to the market, appropriate STT-MRAM testing is of great importance. In this paper, we demonstrate that conventional STT-MRAM defect modeling, which is based on linear resistors, is too pessimistic in representing the real nature of physical defects. It may result in incorrect fault models, which in turn can lead to low-quality test solutions. In addition, we propose a generic defect modeling methodology which captures the nonlinear behavior of STT-MRAM defects accurately; a defect is modeled by adjusting the affected STT-MRAM technology parameters. The methodology is illustrated by two examples, namely a pinhole defect and a sidewall redeposition defect, which are simulated for accurate fault modeling. In case of a pinhole defect, the STT-MRAM suffers from a fast transition between magnetic tunnel junction (MTJ) states with increased write current, making the MTJ more vulnerable to breakdown. However, with the conventional linear resistor as defect model the memory shows a slow transition or even a transition failure. Similarly, a sidewall redeposition defect causes a fast transition without current elevation, which is not observed when using the conventional approach.