This paper proposes a method to estimate basic material constants in an elasto-plastic-creep constitutive model for lead-free solders by conducting only a tensile test. The test employs a stepped ramp wave loading, which repeats instantaneous strain and strain maintenance. Time-independent strains are obtained from the stress-strain relations at the instantaneously strained parts, while the time-dependent strains are obtained from the stress-time relations during the strain maintaining periods. Based on the obtained time-independent and time-dependent strains, the values of the material constants in the elasto-plastic-creep model proposed by the authors are determined. Simulations of the viscoplastic deformations of a Sn–3.0Ag–0.5Cu solder alloy are also conducted to verify the validity of the proposed method.