Alexander McDowell McCook (April 22 1831 - 1903) was an American general who served in the United States Army both as a volunteer and regular officer in the Civil War.

He was born in Columbiana County, Ohio, into the McCook family of who many served in the war. He graduated from the U.S. Military Academy in 1852, served against the Apaches and Utes in New Mexico in 1853-57, was assistant instructor of infantry tactics at the military academy in 1858-1861, and in April 1861 became colonel of the 1st Ohio Volunteers . He served in the first Battle of Bull Run; commanded a brigade in Kentucky in the winter of 1861, a division in Tennessee and Mississippi early in 1862, and the 1st Corps in Kentucky in October of the same year; was in command of Nashville in November and December of that year; and was then engaged in Tennessee until after the battle of Chickamauga, after which he saw no active service at the front during the Civil War.

He was promoted to be brigadier general of volunteers in September 1861, and to be major general of volunteers in July 1862, earned the brevet of lieutenant colonel in the regular army at the capture of Nashville, Tennessee, that of colonel at Shiloh, and that of brigadier-general at the battle of Perryville, and in March 1865 was breveted major-general for his services during the war. In February-May 1865 he commanded the district of Eastern Arkansas.

McCook resigned from the volunteer service in October 1865 and was commissioned lieutenant-colonel of the 26th Infantry in March 1867. He served in Texas, mostly in garrison duty, until 1874. From 1886-1890 (except for brief terms of absence) commanded Fort Leavenworth, Kansas, and the infantry and cavalry school there.

He became a brigadier-general in 1890, a major-general in 1894, and retired in 1895. In 1898-1899, McCook served on a commission to investigate the United States Department of War as administered during the war with Spain.