During the 1970s, Murray dismantles then rebuilds the compositional strategies and theories associated with Minimalism. Her thickly painted and layered compositions introduce geometric forms using curved lines and complex shapes loosely informed by mathematical ideas that transform scale, shape, and form.

Exhibits her Empire State Building series at Fairleigh Dickinson University (’70). The series of sixteen works includes paintings, drawings, and small hand-painted souvenirs all featuring decoratively framed Pop renderings and scenarios of the Empire State Building. Shifting towards a more hard-edged abstraction, Marcia Tucker selects her work for inclusion in the Whitney Museum of American Art's Annual Exhibition (’72). This is Murray’s first participation in a major museum show. Begins exhibiting at the Paula Cooper Gallery (’74). First solo exhibition at Paula Cooper Gallery (’76) with subsequent solo two years later (’78). Solo exhibition at Phyllis Kind Gallery, Chicago features a series of star shaped canvases (’78). Children Meeting is included in the Whitney Biennial and is subsequently purchased by the museum, making the painting the first major acquisition by an American institution (’78).

Group exhibitions during this decade include: Early Work by Five Contemporary Artists: Ron Gorchov, Elizabeth Murray, Dennis Oppenheim, Dorothea Rockburne, Joel Shapiro at New Museum of Contemporary Art, New York (’77); New Painting | New York: Jake Berthot, Ross Bleckner, Alan Cote, Philip Guston, Elizabeth Murray, Jerry Zeniuk, Joseph Zucker at Hayward Gallery, London (’79); American Painting: The Eighties, Grey Art Gallery, New York (’79).