nowrap | |- ! | Jack Brooks | | Democratic | 1952 | Incumbent re-elected. | nowrap | |- ! | Lindley Beckworth | | Democratic | 1956 | Incumbent re-elected. | nowrap | |- ! | Sam Rayburn | | Democratic | 1912 | Incumbent re-elected. | nowrap | |- ! | Bruce Alger | | Republican | 1954 | Incumbent re-elected. | nowrap | |- ! | Olin E. Teague | | Democratic | 1946 | Incumbent re-elected. | nowrap | |- ! | John Dowdy | | Democratic | 1952 | Incumbent re-elected. | nowrap | |- ! | Albert Thomas | | Democratic | 1936 | Incumbent re-elected. | nowrap | |- ! | Clark W. Thompson | | Democratic | 1947 | Incumbent re-elected. | nowrap | |- ! | Homer Thornberry | | Democratic | 1948 | Incumbent re-elected. | nowrap | |- ! | William R. Poage | | Democratic | 1936 | Incumbent re-elected. | nowrap | |- ! | Jim Wright | | Democratic | 1954 | Incumbent re-elected. | nowrap | |- ! | Frank N. Ikard | | Democratic | 1951 | Incumbent re-elected. | nowrap | |- ! | John Andrew Young | | Democratic | 1956 | Incumbent re-elected. | nowrap | |- ! | Joe M. Kilgore | | Democratic | 1954 | Incumbent re-elected. | nowrap | |- ! | J. T. Rutherford | | Democratic | 1954 | Incumbent re-elected. | nowrap | |- ! | Omar Burleson | | Democratic | 1946 | Incumbent re-elected. | nowrap | |- ! | Walter E. Rogers | | Democratic | 1950 | Incumbent re-elected. | nowrap | |- ! | George H. Mahon | | Democratic | 1934 | Incumbent re-elected. | nowrap | |- ! | Paul J. Kilday | | Democratic | 1938 | Incumbent re-elected. | nowrap | |- ! | O. C. Fisher | | Democratic | 1942 | Incumbent re-elected. | nowrap | |- ! | Robert R. Casey | | Democratic | 1958 | Incumbent re-elected. | nowrap | |} Utah |- ! | Henry Aldous Dixon | | Republican | 1954 | | Incumbent retired.New member elected.Democratic gain. | nowrap | |- ! | David S. King | | Democratic | 1958 | Incumbent re-elected. | nowrap | |} Vermont |- ! | William H. Meyer | |