He served as General Riley's chief of staff to Major Folliott T. Lally's column on the march from Vera Cruz to Mexico City in 1847.

[2] From 1862 to 1865, during the American Civil War, Alvord was at Fort Vancouver as the commander of the District of Oregon with the rank of brigadier general of volunteers.

Wright wanted an experienced Regular Army officer in that post, rather than a volunteer, since the District was large (encompassing the present-day states of Oregon, Washington, and Idaho), underdeveloped, and had a history of friction between the native peoples and settlers.

As commander of the District, Alvord built up the defenses around the mouth of the Columbia River, but was unable to do the same for Puget Sound.

In 1882, when he found that there are 96 circles which cut four given circles at a fixed angle and there are 640 spheres which cut five given spheres at a fixed angle, he assembled all his results for an article in American Journal of Mathematics,[6] where he explained the delay: The article is graced with annotations by Arthur Cayley and the concession that Darboux had preceded Alvord in print.

His daughter Louise married Thomas Craig, one of the main professors of mathematics at Johns Hopkins University during its first two decades.

He and his wife Emily Louise Mussey (1826–1885) are buried at Evergreen Cemetery, Rutland, Vermont, Section 4, Lot 4.