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In assessing the insulation withstand level of the electric power apparatus, the step-up test method is used. However, there are still many unknown matters regarding the treatment of the results. In this paper, we assume that the underlying probability distribution of failure time with a constant voltage level follows a Weibull distribution and that there is an inverse power law relationship between the mean lifetime and the imposed voltage, that is, the Weibull power law holds. Under such a condition, we investigate whether we can estimate the unknown parameters using the results obtained by the step-up test. In dealing with the step-up test data, we assume two models: the cumulative exposure model (CEM) and the independence model (IM). In parameter estimation, we use two methods: the maximum likelihood estimation (MLE) method and the method of least squares (LS). The estimates obtained by using the MLE have markedly smaller estimating errors than those by using the LS in both the models of the CEM and IM. While the MLE has a property of the consistency, the LS does not have it. In applying the CEM we can obtain the power law constant and the Weibull shape parameter simultaneously; however, in applying the IM, we cannot do that.