In latest CMOS technologies, Random Telegraph Noise (RTN) has emerged as an important challenge for SRAM design. Due to rapidly shrinking device sizes and heightened variability, analytical approaches are no longer applicable for characterising the circuit-level impact of non-stationary RTN. Accordingly, this paper presents SAMURAI, a computational method for accurate, trap-level, non-stationary analysis of RTN in SRAMs. The core of SAMURAI is a technique called Markov Uniformisation, which extends stochastic simulation ideas from the biological community and applies them to generate realistic traces of non-stationary RTN in SRAM cells. To the best of the authors knowledge, SAMURAI is the first computational approach that employs detailed trap-level stochastic RTN generation models to obtain accurate traces of non-stationary RTN at the circuit level.