The invention provides a flexible mechanical arm mechanism driven by shape memory alloy (SMA) wires and a flexible mechanical arm thereof, and the mechanism and the mechanical arm belong to the technical field of robots. The flexible mechanical arm mechanism comprises an inner layered mandril (1), an outer layered flexible sleeve (2) and a lead bundle (3) which is used for electrically heating the SMA wires, wherein the inner layered mandril (1) comprises a base (105), a top end fixing piece (103), N inner spacers (101), N+1 inner silicone tubes (102) and three SMA wires; the outer layered flexible sleeve (2) comprises a bottom end connecting seat (206), a top end connecting seat (203), M outer spacers (201), M+1 outer silicone tubes (204) and six SMA wires; the inner layered mandril and the outer layered flexible sleeve are connected through a bearing; and the flexible bending movement and the contraction movement of the inner layered mandril are transmitted onto the outer layered flexible sleeve through the bearing.