Probability levels, in the form of marginal cumulative distribution functions, are determined for the time it takes salt to contact a casing, which penetrates a salt canopy, and the time it takes the casing to yield once salt has contacted the casing, in support of through-salt well design activities required for deep-water, sub-salt environments. The finite-element method coupled with an advanced reliability method is used to perform the analyses. Randomness caused by uncertainties in salt properties, lithostatic stress, drilling-mud pressure, production temperature, and borehole ellipticity is handled by including statistics and probability distributions for each of these random variables. The advanced reliability method takes full account of the random variables and processes without Monte Carlo simulation, by using a method for assessing reliability statistics that computes response probabilities in a direct and efficient manner. This advanced reliability method falls under the general category of fast probability integration schemes.