To provide a compact shell-type heat exchanger with the large heat radiation area of a core and improved heat exchange performance in a shell-type heat exchanger.

A baffle plate 6 is arranged in a pair of dish-shaped plates 7 for composing elements 8. Then, a plurality of stages of elements 8 are laminated to compose a core 9, which is accommodated in a shell 5. A peripheral fixing part and a central rising part 13 are formed at each of the disk-shaped plates 7, an annular space 22 is formed at the inner surface side, and at the same time a circular space 23 is formed at the outer surface side of the central rising part 13. Further, an annular flange part 15 for spacer is provided at the bottom end of the central rising part 13. Then, a second fluid 19 is circulated from an outlet/inlet hole 4 of a pipe plate 3 of the shell 5 into each of the elements 8, and a first fluid 18 is circulated from a first fluid outlet/inlet 1 of the shell 5.