His first three seasons Bama experienced nothing but frustration at the hands of the Vols. In three consecutive years the Tide dropped close decisions, 34-41 in 1983, 27-28 in '82 and 14-16 in '85. Three losses by a total of only 10 points.
But Shula's senior year was different. Ending a 4-0 run by Tennessee, the Tide demolished UT 56-28. And the final score was much closer than the game itself.
"The game comes at such a pivotal time during the season," Shula commented. "When we beat them that fourth year (1986), it was after three years of frustration. We felt like if we beat them we had a chance to finish strong. That game felt good."
Shula was there and healthy, so the Tide had plenty of firepower at its disposal throwing the football. But Bama won that game on the strength of its rushing attack. Toss sweep after toss sweep, the Tide buried a previously well-regarded Volunteer defense.
And it wasn't even close.
The Tide backs got to the edge of the Volunteer 'D' time after time, play after play, gaining yardage in impressive chunks. 12 yards here, eight yards there, 14 more yards this time. With then-sophomore Bobby Humphrey doing most of the damage, Bama's running backs made it look easy.
In the third quarter with Bama already up 56-14 and seemingly headed for more, Tennessee press-box workers were busily thumbing through old records, fully expecting the final margin to approach historic proportions.
Has Shula ever been involved in a game where one team relied so exclusively on the run, hardly even bothering to throw the football?
"Two weeks ago was pretty close against Southern Miss," Shula said, recalling Bama's last win with a smile.
Earlier in the press conference Shula had made a standard statement about Bama's upcoming opponent, observing that you couldn't expect to beat Tennessee by just running or passing the football. Alabama's offense would have to be balanced to have a chance to win.
What about what happened in 1986, Coach?
"You can't live in the past," Shula replied with a smile.
Certainly not without Bobby Humphrey in the backfield. Humphrey gained 217 yards that day before Coach Ray Perkins called off the troops.
"Six times we threw the ball that day," Shula continued, recalling Bama's 56-28 win that day. "You don't ever know. Who would have ever guessed that game would have turned out like that? Who would have ever guessed the streaks would have gone like that?"
Bama's '86 victory started an 8-0-1 streak of its own. Tennessee responded by winning the next seven, before Bama won in Knoxville last year 34-14.
"That (1986) win started a streak," Shula said. "Last year Alabama ended a streak. I've watched this series for years as an alumni.
"The most predictable thing is that this series is unpredictable."