A hot bulge forming die apparatus forms a preheated tubular material 10a into a tubular material 10d. The hot bulge forming die apparatus includes a lower die 21B having a cavity surface 211B and an upper die 31B having a cavity surface 311B. An elongated hole 215 is formed in a circumferential edge portion 215 of the lower die 21B so as to extend outwards, and a projection 315 is formed on a circumferential edge portion 314 of the upper die 31B so as to fit in the elongated hole 215. When the dies are clamped together, the projection 315 formed on the circumferential edge portion 314 of the upper die 31B fits in the elongated hole 215 formed in the circumferential edge portion 214 of the lower die 21B.