The support system of an thin primary mirror consists of axial supports and lateral supports. Lateral supports mainly support the component force of the mirror’s gravity normal to the optical axis of the mirror. The push- pull- shear lateral support and the principle of active correction are introduced, and 5 alternative lateral supports are designed for an 8 m active thin mirror. Taking account of the active correction of the primary mirror and comparing the 5 alternatives via the finite element method, the best lateral support of the 8 m mirror is determined. The best lateral support consists of 64 lateral support points, and each point only applies an tangential force. The root mean square of the surface of the 8 m mirror after active correction is 19.2 nm when the mirror is mounted vertically and the range of the correction forces is - 318.9~301.4 N. Compared with regular push- pull- shear lateral support, this lateral support is simpler in structure, easier to implement and has good supporting performance.