Gaussian time-varying loading induces Gaussian components of the stress tensor in a linear structure, where the loading is assumed stationary. For any stress component, finite element spectrum analysis obtains the standard deviation, and any percentile can be calculated as a multiple of the standard deviation. However, a yield criterion requires a percentile of von Mises stress. The distribution of von Mises stress arising from random vibration loading stymies closed-form characterization, but several algorithms estimate its percentiles. One algorithm treats combined random vibration and static loadings. This paper improves computational efficiency for special plane stress cases, e.g., combining finite element spectrum and static analyses of piping models. All the algorithms are applied to a simple test model. Results match Monte Carlo simulation. Computational efficiencies are evaluated and compared.