Since guided waves propagate with very complex behavior, numerical calculations with a semi-analytical finite element (SAFE) method have become widely used as the most efficient calculation technique for guided waves in an elongated structure. However, a problem of leaky guided waves is not handled with the SAFE although energy attenuation by leak is a crucial issue in practical guided wave inspections. In this study, we formulated the SAFE for Lamb waves in a plate leaking to fluid, and dispersion curves of phase velocity and attenuation were calculated for an aluminum plate surrounded by water. The calculation results agreed well with ones in the previous theoretical studies, which show that the calculations of leaky Lamb waves with the SAFE were carried out with sufficient accuracy.