In 1992 K. Wirthmuller proved an analogue of the Chevalley theorem for weak Jacobi forms associated with irreducible root systems, except $E_8$. However, generators in his proof are not constructed explicitly, but they are important in applications. In my talk, I will discuss the new simple approach to this problem in cases of root systems D_n and F_4. Following this method, it is possible to construct the generators of the corresponding algebras of weak Jacobi forms using only Jacobi theta functions and modular differential operators.