Mathieu used admissible highest weight modules of finite dimensional Lie algebras to determine all torsion free modules. There is a natural analogue of admissible modules for affine Lie algebras. We use the work of Chari, Chari and Pressley and of Rao to construct all admissible modules for non-twisted affine algebras. This involves the construction of all simple highest weight modules for $A_1^{(1)}$in $\tilde{O}$ having finite dimensional weight spaces. We believe that this construction will actually produce all simple highest weight modules in $\tilde{O}$ having finite dimensional weight spaces for arbitrary non-twisted affine algebras. This is joint work with Frank Lemire