The notion of quasiconvex exposed points is introduced for compact sets of matrices, motivatedfrom the variational approach to material microstructures.We apply thenotion to give geometric descriptions of thequasiconvex extreme points for a compact set. A weak version of Straszewicz typedensity theorem in convex analysis is established for quasiconvex extreme points. Some examplesare examined by using known explicit quasiconvex functions.