An　p　x　q　matrix　A　is　said　to　be　(M,　N)-symmetric　if　MAN　=　(MAN)(T)　for　given　M　is　an　element　of　R-nxp,　N　is　an　element　of　R-qxn.　In　this　paper,　the　following　(M,　N)-symmetric　Procrustes　problem　is　studied.　Find　the　(M,　N)-symmetric　matrix　A　which　minimizes　the　Frobenius　norm　of　AX　-　B,　where　X　and　B　are　given　rectangular　matrices.　We　use　Project　Theorem,　the　singular-value　decomposition　and　the　generalized　singular-value　decomposition　of　matrices　to　analysis　the　problem　and　to　derive　a　stable　method　for　its　solution.　The　related　optimal　approximation　problem　to　a　given　matrix　on　the　solution　set　is　solved.　Furthermore,　the　algorithm　to　compute　the　optimal　approximate　solution　and　the　numerical　experiment　are　given.　(C)　2007　Elsevier　Inc.　All　rights　reserved.