In this work, tensile creep tests for Sn-1.0Ag-0.5Cu-0.02Ni solder have been conducted at various temperatures and stress levels to determine its creep properties. The effects of stress level and temperature on creep strain rate were investigated. Creep constitutive models (such as the simple power-law model, hyperbolic sine model, double power-law model, and exponential model) have been reviewed, and the material constants of each model have been determined based on experimental results. The stress exponent and creep activation energy have been studied and compared with other researchers’ results. These four creep constitutive models established in this paper were then implemented into a user-defined subroutine in the ANSYS™ finite-element analysis software to investigate the creep behavior of Sn-1.0Ag-0.5Cu-0.02Ni solder joints of thin fine-pitch ball grid array (TFBGA) packages for the purpose of model comparison and application. Similar simulation results of creep strain and creep strain energy density were achieved when using the different creep constitutive models, indicating that the creep models are consistent and accurate.