In this paper, we review the production cross section for charged and neutral Higgs bosons pairs in $e^{+}e^{-}$ collisions beyond the tree level, in the framework of the Minimal Supersymmetric Standard Model (MSSM). A complete list of formulas for all electroweak contributions at the one loop level is given. A numerical code has been developed in order to compute them accurately and, in turn, to compare the MSSM Higgs bosons pair production cross sections at tree level and at the one loop level.