Lateral–directional stability is a critical issue for the design of any kind of aircraft. For the hypersonic waverider, the nonaxisymmetric, flat, and slender geometric feature makes it susceptible to the problem of lateral–directional instability. Therefore, the influence of geometric feature on the lateral–directional static and dynamic stability of hypersonic waverider is studied so as to enable the designer to consider this problem in the preliminary aircraft design stage. A series of power-law waveriders is generated at a given design space of the leading-edge parameters. Then, the variation of the static and dynamic derivatives with the design parameter is obtained by use of a surrogate model. It is found that increasing the dihedral angle of the lower surface can improve both the lateral and directional static stability of the total waverider. Furthermore, the dynamic instability mechanisms are analyzed in detail based on the approximate formulas derived from the linearized small-disturbance equations of motion. Especially, a concept of the Dutch-roll dynamic derivative CnpDYNCnpDYN is proposed, which plays an important part in the damping of the Dutch roll. Finally, it is found that increasing the dihedral angle can also improve the damping of the dynamic modes, including the roll, spiral, and Dutch roll.