Raised in Detroit, Marshall pursued autodidactic interests in history, literature and the natural and social sciences from a young age. He graduated from Cass Technical High School (where he trained in machining and received the second-highest score on a citywide aptitude test for honors students similar in provenance to the SAT) in 1939. After briefly working in a factory and attending the University of Detroit for a year, he dropped out to take a position at the Murray Body Company, where he manufactured machine tools used in fabricating British airplane parts. Unable to serve in World War II due to a heart murmur, Marshall continued to work at Murray for the remainder of the war. He eventually resumed his formal studies at Wayne State University in 1943.
Marshall was admitted to the University of Chicago with graduate standing in 1945; under the chancellery of Robert Maynard Hutchins, students who were not enrolled in the generalist "Chicago Plan" undergraduate program pursued a course of study that led to a master's degree. Strongly influenced by Friedrich Hayek, he earned an M.A. in economics from the institution in 1949. His master's thesis was a sensitivity analysis of Lawrence Klein's econometric model of the US economy; influential for its methodology, it has never been published except for a short abstract.
After electing to defer his studies in favor of eventually pursuing a Ph.D. in statistics (a program not yet offered by the University of Chicago), Marshall joined the RAND Corporation, the original "think tank," at the behest of mentor W. Allen Wallis in 1949. While he would briefly return to academia to cover Wallis's courses during the 1953-1954 term and continued to take statistics courses at George Washington University, Marshall soon gained the cachet of being part of "a cadre of strategic thinkers" that coalesced at the RAND Corporation in the 1950s and 1960s, a group that also included Charles J. Hitch, Herman Kahn, James Schlesinger and Daniel Ellsberg. Notably, he worked with Kahn on developing and advancing Monte Carlo methods.
Schlesinger would later become the U.S. Secretary of Defense and personally oversaw the creation of the Office of Net Assessment. The original main task of the office was to provide strategic evaluations on nuclear war issues. James Roche, Secretary of the Air Force in the administration of George W. Bush, worked for Marshall during the 1970s.
Andrew Marshall was consulted for the 1992 draft of Defense Planning Guidance (DPG), created by then-Defense Department staffers I. Lewis Libby, Paul Wolfowitz, and Zalmay Khalilzad.
Marshall has been noted for fostering talent in younger associates, who then proceed to influential positions in and out of the federal government: "a slew of Marshall's former staffers have gone on to industry, academia and military think tanks." Dick Cheney, Donald Rumsfeld, and Paul Wolfowitz, among others, have been cited as Marshall "star protégés."
In an interview in 2012 the main author of four of the Chinese defence white papers General Chen Zhou stated that Marshall was one of the most important and influential figures in changing Chinese defence thinking in the 1990s and 2000s.
Foreign Policy named Marshall one of its 2012 Top 100 Global Thinkers, "for thinking way, way outside the Pentagon box".