The 1875–76 Scottish Cup – officially the Scottish Football Association Challenge Cup – was the third season of Scotland's most prestigious football knockout competition. The number of entrants nearly doubled from the previous season with 49 teams included in the first round draw. The competition began on 2 October 1875 and concluded with the final replay on 18 March 1876. This was the first season that teams would only change ends at half time, the tradition of changing ends after a goal had been scored came to an end. The cup was won for the third time by Queen's Park who defeated fellow Glasgow club 3rd Lanark RV 2–0 in the replayed final.

Third Lanark Athletic Club was a Scottish football club based in Glasgow. Founded in 1872 as an offshoot of the 3rd Lanarkshire Rifle Volunteers, the club was a founder member of the Scottish Football Association (SFA) in 1872 and the Scottish Football League (SFL) in 1890. Third Lanark played in the top division of the SFL for the majority of the club's existence, and won the league championship in 1903–04. The club also won the Scottish Cup twice, in 1889 and 1905. Third Lanark went out of business in 1967, as a result of mismanagement, six years after having finished in third place in the SFL. Third Lanark's former ground, Cathkin Park in Crosshill, is still partially standing and is used for minor league football.