Constitutive models for SnAgCu solder alloys are of great interest at the present. Commonly, constitutive models that have been successfully used in the past for Sn-Pb solders are used to describe the behavior of SnAgCu solder alloys. Two issues in the modeling of lead-free solders demand careful attention: (i) Lead-free solders show significantly different creep strain evolution with time, stress and temperature, and the assumption of evolution to steady state creep nearly instantaneously may not be valid in SnAgCu alloys and (ii) Models derived from bulk sample test data may not be reliable when predicting deformation behavior at the solder interconnection level for lead-free solders due to the differences in the inherent microstructures at these different scales. In addition, the building of valid constitutive models from test data derived from tests on solder joints must deconvolute the effects of joint geometry and its influence on stress heterogeneity. Such issues have often received insufficient attention in prior constitutive modeling efforts. In this study all of the above issues are addressed in developing constitutive models of Sn3.8Ag0.7Cu and Sn1.0Ag0.5Cu solder alloys, which represent the extremes of Ag composition that have been mooted at the present time. The results of monotonic testing are reported for strain rates ranging from 4.02E-6 to 2.40E-3 s-1. The creep behavior at stress levels ranging from 7.8 to 52 MPa are also described. Both types of tests were performed at temperatures of 25°C, 75°C and 125°C. The popular Anand model and the classical time-hardening creep model are fit to the data and the experimentally obtained model parameters are reported. The test data are compared against other reported data in the literature and conclusions are drawn on the plausible sources of error in the data reported in the prior literature.