The dispersion and attenuation of Lamb and Leaky Lamb waves propagating in a 1 mm-thick steel plate were investigated. For acquiring a long(or large) range inspection capability, the fundamental symmetric and anti-symmetric wave modes(S0 and A0) over law frequencies were studied. Based on the dispersion curves, as well as pitch-catch and multi-mode simulations, it was shown that the S0 mode over law frequencies is the proper mode to minimize the dispersion and attenuation. In addition, it was shown that the S0 mode couldbe easily distinguished under multi-mode simulation since it has a larger group velocity than the A0 mode.