As technology scales to smaller dimensions, increasing process variations, coupling induced delay variations and multiple input switching effects make timing veri cation extremely challenging. In this paper we establish a theoretical framework for statistical timing analysis with coupling and multiple input switching. We prove the convergence of our proposed iterative approach and discuss implementation issues under the assumption of a Gaussian distribution for the parameters of variation. A statistical timer based on our proposed approach is developed and experimental results are presented for the ISCAS benchmarks. We juxtapose our timer with a single pass, non iterative statistical timer that does not consider the mutual dependence of coupling with timing and another statistical timer that handles coupling deterministically. Monte Carlo simulations reveal a distinct gain (up to 24%,) in accuracy by our approach in comparison to the others mentioned.