The fission cross sections have been measured for U233 and U238 targets bombarded with 18 to 43 Mev helium ions. These targets were chosen because of their large fission cross sections. In addition, the spallation cross sections are known and represent with 43-Mev helium ions only about 4 and 9% of the reaction cross sections of U233 and U238, respectively. The fission fragments were detected with solid-state counters in a small evacuated scattering chamber. The fission fragment counting rates were converted to disintegration rates with previous measurements of the fission fragment angular distributions. The experimental reaction cross sections are in good agreement with reaction cross sections calculated with an optical model in which the complex nuclear potential derived by Igo for alpha-particle elastic scattering is employed. The dependence of the optical model cross sections on the various Woods-Saxon parameters is discussed.