The scattered fields of Lamb waves resulting from damage have been extensively studied because they carry rich structural information that allow us to identify and evaluate damage. This paper investigates the interaction of the fundamental symmetric Lamb mode (S0) near the first Lamé point with opening cracks of various heights under the plane strain condition. The scattering coefficients obtained by the semi-analytical method indicate a significant non-mode-conversion point, where the mode conversion is very weak. The frequency of this non-mode-conversion point originates in the first Lamé point and increases linearly with the crack height when the normalized height is less than 25%. The finite element simulations validate the calculation results. In addition, similar phenomena are also observed for the scattering at a symmetric internal crack. These interesting scattering characteristics are related to the special mode shapes near the Lamé point, which may provide a candidate to evaluate the height of an opening crack.