A series of SnBi alloys with Bi concentration ranging from 3% to 70% have been studied by nanoindentation technique at room temperature. Constant strain rate (CSR) method was used to evaluate the elastic modulus, hardness and the creep stress exponent of the alloys. SnBi solid solutions with Bi concentration up to 10 wt% show significantly higher modulus and hardness than pure Sn. Small amount of Bi precipitates inside Sn-rich phase effectively enhance the hardness and creep resistance of the alloy; while such distribution of Bi particles has no effect on the elastic response of the matrix. The strain rate–stress relationship of the SnBi alloys has been evaluated in the range from 90 to 450 MPa. Three stress regions dominated by different rate-controlling mechanisms exist for the SnBi alloys with Bi concentration greater than 10%. At the high stress region (>370 MPa), dislocation glide dominates the creep rate where the stress exponents are greater than 10. At the intermediate stress region (200–370 MPa), dislocation climb is the dominant creep mechanism with stress exponents around 5–8. When fine lamellar structure is the dominant constituent of the microstructure, phase boundary sliding is identified as the rate-controlling mechanism in the low stress region (<200 MPa).