Alexandrakis graduated from the School of Fine Art, Athens in 1937, having won all the major art awards; those of Portrait, Nude, Semi-nude and Composition. His achievements are considered unique in the history of the annual prize of the school.

He is an artist of international repute, having forged a strong reputation in the USA where he regularly submitted work to The Guggenheim in New York for its annual exhibition. In 1950 he submitted two works for the design of a poster for the Marshal Plan, organised by the American Government. He won the first and second prize.

Alexandrakis’ military drawings and paintings were exhibited publicly for the first time in 1946, in the art space at 27, Ermou Steet. They were received by the art loving public and press as a unique event to celebrate the National Epos of 1940-1941. The second exhibition of military works took place in 1958 at the artist’s studio in Notata Street, Exarchia.

In 1980 The National Gallery, Athens organised a retrospective exhibition on Alexandrakis, highlighting the war paintings and later in 1995 an exhibition commemorating the 50th Anniversary of the end of the war was organised at The Hellenic Centre, London, titled The War we Fought 1940-41, Paintings and Drawings by A. Alexandrakis

In 2011 the 'Melina' Cultural Centre, Athens, staged the exhibition Memories of the 1940s, Alexandros Alexandrakis, where the entire collection of military works on paper and canvas were exhibited.

His work can be found in many public and private collections in Greece and Cyprus. Notably at The National Gallery Greece, The Municipality of Athens, The State Gallery of Contemporary Cypriot Art, The Leventis Gallery, The Bank of Cyprus Cultural Centre Foundation, The Hellenic War Museum.