The solder joint in electronic packages is increasingly miniaturized to achieve the high-density mounting of electronic parts. Such a miniaturized solder joint is thought to have different deformation characteristics from bulk solder specimens. Therefore, the finite element analysis for evaluating the strength reliability of the miniaturized solder joint should employ the material parameters estimated by conducting the test with miniature solder specimens. In addition, the material parameters must be estimated in a short period because the development period for electronic devices tends to become shorter. One of the authors has proposed an experimental method termed tension-strain maintenance test which can estimate the material parameters for viscoplastic material such as solder in a short time. Then, in this work, by applying the method to a miniature solder specimen, we estimated the material parameters which represent the elasto-plastic and creep characteristics of the specimen. Using a constitutive model with the estimated parameters, some simulations of the tensile tests with the miniature solder specimens were conducted to verify the availability of the estimation method.