Ab initio total-energy calculations were used to examine (2\ifmmode\times\else\texttimes\fi{}2) reconstruction models for the (111) and (1\ifmmode\bar\else\textasciimacron\fi{}1\ifmmode\bar\else\textasciimacron\fi{}1\ifmmode\bar\else\textasciimacron\fi{}) surfaces of GaAs. For the (111) surface the lowest-energy Ga-vacancy geometry is determined; several mechanisms for Ga-vacancy formation are examined and other reconstructions are discussed. For the (1\ifmmode\bar\else\textasciimacron\fi{}1\ifmmode\bar\else\textasciimacron\fi{}1\ifmmode\bar\else\textasciimacron\fi{}) surface it is shown that the As-vacancy model is unlikely and other geometries are considered.