Finney's debut came in 1971, when he competed at Richmond. Starting 28th in the field of thirty, Finney fell many laps down in the race in route to a 21st place showing.
Finney's next start, which came in 1972, was also at Richmond. Starting 20th in the field of sixteen, Finney was this time able to better his finish to 16th despite losing a fan belt late in the race.
Finney also competed in a lone event during the 1973 season, competing at Talladega. Starting 43rd in the field of fifty, Finney logged just fifty-five laps in the show before finishing 41st.
Finney's 1974 one-off start would again come at Talladega. Again, engine woes found the driver, allowing him to just make the 100-lap in route to finishing 31st.
Finney did not return to the sport until 1977, when he made an appearance at Atlanta. Engine issues found their way to his car yet again, as the driver started and finished 35th.
Finally, Finney made his final two races in 1980. DNFs appeared yet again in Finney's record books. Engine failure was three-for-three with Finney at Talladega, when he broke on lap thirty-six to finish 38th. He fared a bit better in his final start, crashing late but still finishing 20th in the July event at Daytona.