Granata's work was included in the groundbreaking 1959 traveling exhibition Recent Sculpture U.S.A. at the Museum of Modern Art, MoMA, New York, alongside Ruth Asawa, Alexander Calder, John Chamberlain, Jacques Lipchitz, Larry Rivers, David Smith, ... many of whom instrumental in rewriting American post-war Art History.

Over the course of his 60 year long artistic career, his work work was included in exhibitions at Museum of Modern Art, New York City; Forum Gallery, New York City; the Boston Museum of Art; the Los Angeles Museum of Art ; the Denver Museum of Art; the St Louis Museum of Art; the Birmingham Museum of Art; the Delgado Museum of Art (now the New Orleans Museum of Art); the Wichita Museum of Art in Wichita, KS; the Des Moines Museum of Art in Des Moines, IA; the Ringling Museum of Art, Sarasota, FL; the Hunter Museum of Art, Chattanooga, TN; the Mint Museum, Charlotte, NC; as well as at the Departamento de Arte Yucatán in Mèridia, Yucatán, Mexico; and the Centro Colombo Americano, Cali, Colombia.