Commonly, constitutive models of solder alloys are derived from mechanical tests performed on either bulk solder specimens or on specially assembled BGA test coupons where the stresses are borne by solder ball interconnects. It has been widely recognized that models derived from bulk sample test data may not be reliable when predicting deformation behavior at the solder interconnect level due to the differences in the inherent microstructures at these different scales. This is particularly critical for lead-free SnAgCu solder alloys owing to their complex microstructures. There are two primary challenges associated with developing models from solder interconnect level test data: the experimental complexity associated with accurately resolving and controlling displacement at the scale of the interconnection, and the non-uniformity of stresses inherent in the solder interconnection geometry. In testing at interconnection level, published studies have used testing techniques that don't control deformation at the interconnect and have made uniformity of stress (and strain) approximations that are mostly invalid. Developing constitutive models from such data can produce erroneous results. In this study, we first demonstrate tests that control deformation at the interconnection level. We then show how heterogeneous stress distribution in solder interconnects can significantly affect the constitutive modeling of solder alloys and describe the conditions under which approximations may be made in the determination of accurate constitutive models. We validate our approach through experimental testing on Sn3.8Wwt%Ag0.7Wt%Cu solder joints and finite element analysis.