Strain elastography (SE) is a technique in which images of localized tissue strains are used to detect the relative stiffness of tissues. The application of SE in differentiating malignant breast lesions from benign ones has been broadly investigated. The strain ratio between the background and the breast tumor has been used and its results have been mixed. Due to the complex nature of tissue elasticity and how it relates to the strain fields measured in SE, the exact reason is not known. In this study, we apply a novel design-of-experiments based metamodeling approach to mechanical simulation of SE in the human breast. To our knowledge, such a study has not been reported in the ultrasound SE literature. More specifically, we first conduct a screening study to identify the biomechanical factors/simulation inputs that most strongly determine strain ratio. We then apply a response surface experimental design to these factors to produce a meta-model of strain ratio as a function of said factors. Results from the screening study suggest that the strain ratio measurements are primarily influenced by 3 factors: the initial shear modulus of the lesion, the elastic nonlinearity of the lesion and the precompression applied during acquisition. In order to investigate the implications of these results, stochastic inputs for these 3 factors associated with malignant and benign cases were applied to the resulting response surface. The resulting optimal cut-offs, sensitivity, and specificity were generally in line with a majority (> 60%) of 19 clinical trials in the literature.