In　this　paper,　the　class　of　multivariate　extended　skew　normal　distributions　is　introduced.　The　properties　of　this　class　of　distributions,　such　as,　the　moment　generating　function,　probability　density　function,　and　independence　are　discussed.　Based　on　this　class　of　distributions,　the　extended　noncentral　skew　chi-square　distribution　is　defined　and　its　properties　are　investigated.　Also　the　necessary　and　sufficient　conditions,　under　which　a　quadratic　form　of　the　model　has　an　extended　noncentral　skew　chi-square　distribution,　are　obtained.　For　illustration　of　our　main　results,　several　examples　are　given.　©　Springer　International　Publishing　Switzerland　2016.