Linear　mixed　effects　models　with　general　skew　normal-symmetric　(SNS)　error　are　considered　and　several　properties　of　the　SNS　distributions　are　obtained.　Under　the　SNS　settings,　ANOVA-type　estimates　of　variance　components　in　the　model　are　unbiased,　the　ANOVA-type　F-tests　are　exact　F-tests　in　SNS　setting,　and　the　exact　confidence　intervals　for　fixed　effects　are　constructed.　Also　the　power　of　ANOVA-type　F-tests　for　components　are　free　of　the　skewing　function　if　the　random　effects　normally　distributed.　For　illustration　of　the　main　results,　simulation　studies　on　the　robustness　of　the　models　are　given　by　comparisons　of　multivariate　skew-normal,　multivariate　skew　normal-Laplace,　multivariate　skew　normal-uniform,　multivariate　skew　normal-symmetric,　and　multivariate　normal　distributed　errors.　A　real　example　is　provided　for　the　illustration　of　the　proposed　method.