The invention relates to a support device for the gun sight of a military vehicle, incorporating a head to which the gun sight is fastened and a foot which is integral with the vehicle, the head being integral with a column with a vertical axis which is introduced into the foot, the column being made integral with the foot by spring means wherein the spring means are constituted in the form of tongues arranged along at least two parallel planes perpendicular to the vertical axis of the support, each plane incorporating at least three tongues evenly spaced angularly around the column and integral with it by a first end and integral with the foot by their second end, these spring means imparting stiffness to the link between the column and the foot that is less along the vertical axis than along the other directions (X, Y) orthogonal to this vertical axis.