The first Landau constant of a free shear layer with parallel velocity profileU=tanh yis calculated numerically according to the amplitude expansion formulation proposed by Herbert [J. Fluid Mech.126, 167 (1983)]. The numerical results strongly support Gotoh’s asymptotic expression [J. Phys. Soc. Jpn.24, 1137 (1968)] of the first Landau constant &lgr;1for large Reynolds numberRwhen the amplification factorciis smaller thanR−1/3: &lgr;1=−8.177R1/3(1+0.25Rci). It is also concluded that the third‐order nonlinear term in the Landau equation acts as the stabilizing effect throughout the parameter range where the numerical calculation was performed.