In this study, elastic buckling criteria for die fins during extrusion of complex-shaped parts are analytically derived. In this analytical model, the fins of the extrusion die are regarded as cantilever beams with a narrow rectangular cross section. The load intensity acting on each fin is assumed to be distributed uniformly, which is quite similar to the actual distribution. The elastic critical load intensity of buckling is successfully obtained by solving simultaneously the moment equilibrium differential equations. A commercial finite element package '' DEFORM 3D '' is also employed to simulate the flow pattern of the billet inside the die in extrusion of a CPU heat sink. The stress distribution pattern on the fins of the extrusion die is discussed.