A recent study shows that the existing first-order canonical timing model is not sufficient to represent the dependency of the gate/wire delay on the processing and operational variations when these variations become more and more significant. Due to nonlinear mapping from variation sources to the gate/wire delay, the distribution of the delay will no longer be Gaussian even if variation sources are normally distributed. A novel "quadratic timing model" is proposed to capture the nonlinearity of the dependency of gate/wire delays and arrival times on the variation sources. Systematic methodology is also developed to evaluate the correlation and distribution of the quadratic timing model. Based on these, a statistical static timing analysis algorithm that retains the complete correlation information during timing analysis and has linear computation complexity with respect to both the circuit size and the number of variation sources is proposed. Tested on the ISCAS circuits, the proposed algorithm shows significant accuracy improvement over the existing first-order algorithm with a small amount of computational cost