| Office: | Mayor of Trondheim |
| Term Start: | 1 January 1976 |
| Term End: | 31 December 1979 |
| Predecessor: | Kaare Tønne |
| Successor: | Olav Gjærevoll |
| Office2: | Deputy Representative in the Norwegian Parliament |
| Term Start2: | 1 October 1981 |
| Term End2: | 30 September 1985 |
| Constituency2: | Sør-Trøndelag |
| Term Start3: | 1 October 1977 |
| Term End3: | 30 September 1981 |
| Constituency3: | Sør-Trøndelag |
| Birth Date: | 10 August 1930 |
| Birth Place: | Trondheim, Norway |
| Death Place: | Inderøy, Norway |
| Party: | Conservative |
| Spouse: | Anne-Kathrine Parow |
Axel Buch (10 August 1930 – 30 July 1998) was a Norwegian politician from the Conservative Party.
He is known as mayor of Trondheim, the third largest city in Norway, from 1976 to 1979.
Buch served as a deputy representative in the Norwegian Parliament from Sør-Trøndelag during the terms 1977 - 1981 and 1981 - 1985.