A stochastic method was devised to transform efficient sets of analytical characterizations into molecular representations of complex petroleum feedstocks. Important structural attributes of petroleum molecules (e.g. number of aromatic rings, number of naphthenic rings, number and length of aliphatic side chains) were assembled into molecules according to quantitative probability density functions for each attribute. The outcome was the atomic detail of a large ensemble of representative molecular structures from which both molecular and global product properties were deduced. Critical steps in the stochastic method were the generation of a chemical logic diagram, the compilation of cumulative probability functions for the structural attributes, stochastic sampling of each distribution, and the molecular construction. A general Monte Carlo algorithm provided an unbiased sampling of the probability density functions. The method was applied to three different complex petroleum feedstock fractions: an offshore California asphaltene, a Kern River heavy oil, and sour import heavy gas oil. The asphaltene example predicted the defining solubility protocol to within 1%. The heavy oil and gas oil simulations reproduced boiling point fractionation curves to within standard deviations of 20.8 and 25°C.