Sn–Ag–Cu, commonly known as SAC, is considered to be among the most promising of all lead-free solder alloys. Research aimed at making electronic components smaller has pointed to the possible use of nanosized solder joints in the future. In this study, for the first time, molecular dynamics simulations were used to analyze the thermomechanical properties of SAC solder materials at the nanoscale. The modified embedded-atom method (MEAM) potential was utilized in the simulations of the SAC solder materials. The dimensions of the structures considered were 55 × 55 × 59 Å. Four different SAC solders were studied, with Ag percentages ranging from 1% to 4% (SAC105, SAC205, SAC305, and SAC405). Thus, the effects of the Ag percentage on the thermomechanical properties of the solder at the nanoscale were identified. The impacts of the temperature on the uniaxial tensile properties and coefficient of thermal expansion (CTE) values of the SAC solder materials were investigated by performing simulations of the materials at different temperatures. Results suggest that as the Ag percentage increases, the uniaxial tensile strength and CTE of the solder increase whereas the failure strain and thermal conductivity decrease. The results presented should prove useful in the electronic packaging industry.