A rack structure for a chair includes a chair back member having a frame and a mounting support. The frame includes a support cushion disposed on the front side thereof for supporting a user's waist correspondingly. The frame further includes two first connecting tabs fixed on the back sides of the top ends of two sides thereof individually and two second connecting tabs formed on and extending from the two sides thereof respectively. The mounting support is fixed onto a base and extends upwardly therefrom. The mounting support includes two coupling segments and two connecting projections arranged on the top ends and the intermediate sections of two sides thereof respectively. Between each coupling segment and each connecting projection is couplingly attached a resilient member. The first and second connecting tabs of the frame are connected with the coupling segments and the connecting projections of the mounting support individually.