He first worked for Lionel Train Company until 1940, developing time and motion studies that so impressed the president that he was made an offer to become CEO (which he turned down). During World War II he was (unbeknownst to himself at the time) a consultant on the Manhattan Project. After the war, he took up teaching at Columbia University. He taught there for 50 years. As he reached retirement as a professor at Columbia, he began volunteering to work with under-privileged minority students from inner-city New York public schools. Developing a hands-on method of teaching kids about the built environment, he was able to reach over thousands of students and teachers, giving them an appreciation of the usefulness of mathematics and science. In 1987 he founded the Salvadori Educational Center on the Built Environment (since renamed the Salvadori Center), a non-profit educational center on the campus of City College of New York which uses the "city as classroom" to help teachers and students master the core subject areas in their curricula.
From 1954 to 1960, Salvadori worked as a consultant and then Principal at Weidlinger Associates, an engineering firm in New York City. He then became a Partner until 1991, when he became honorary chair. As a structural engineer, Salvadori became known for the design of thin concrete shells as he strove to create great architecture in all of his projects.
Salvadori was also the author of many well-respected textbooks, including Structural Design in Architecture (1967),Why Buildings Stand Up (1980), Why Buildings Fall Down (1992), and Why The Earth Quakes (1995). In 1993 Salvadori became the first engineer to receive the American Institute of Architects' Topaz Medallion for Excellence in Architectural Education. Salvadori is also known for his translation of da Vinci's notebooks into English and of Emily Dickinson's poems into Italian.