This paper analyzes similar tests for structural change for the normal linear regression model in finite samples. Using the approach of Wald (1943, American Mathematical Society Transactions 54, 426–482), Hillier (1987, Econometric Theory 3, 1–44), Andrews and Ploberger (1994, Econometrica 62, 1382–1414), and Andrews, Lee, and Ploberger (1996, Journal of Econometrics 70, 9–36), we characterize a class of optimal similar tests for the existence of (possibly multiple) changepoints at unknown times. We extend the analysis of Andrews et al. (1996) by deriving weighted optimal similar tests for the case where the error variance is not known. We also show that when the sample size is large, the tests of Andrews et al. constructed by replacing the error variance with an estimate are equivalent to the optimal test derived in this paper. Power comparisons are provided by a small simulation study.