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The simplest theoretical model is fully characterised by only two parameters: the mass of the dark photon m<jats:inline-formula><jats:alternatives><jats:tex-math>$$_{\\gamma ^{\\mathrm {D}}}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mrow\/>\n                    <mml:msup>\n                      <mml:mi>\u03b3<\/mml:mi>\n                      <mml:mi>D<\/mml:mi>\n                    <\/mml:msup>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and its mixing parameter with the photon, <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\varepsilon $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03b5<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. The sensitivity of the SHiP detector is reviewed for dark photons in the mass range between 0.002 and 10\u00a0GeV. Different production mechanisms are simulated, with the dark photons decaying to pairs of visible fermions, including both leptons and quarks. Exclusion contours are presented and compared with those of past experiments. 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