This paper develops a statistically based computational method to rapidly determine stresses in flexible substrates during particle printing processes. Specifically, substrate stresses due to multiple surface particle contact sites are statistically computed by superposing point load solutions for different random particle realizations (sets of random loading sites) within a fixed feature boundary. The approach allows an analyst to rapidly determine the number of particles in a surface feature needed to produce repeatable substrate stresses, thus minimizing the deviation from feature to feature and ensuring consistent production. Three-dimensional examples are provided to illustrate the technique. The utility of the approach is that an analyst can efficiently ascertain the number of particles needed within a feature, without resorting to computationally intensive numerical procedures, such as the finite element method.