Progress in the calculation of the electronic structure of polyatomic molecules in the Solid State and Molecular Theory Group and the Cooperative Computing Laboratory at M.I.T. is described. This includes the preparation of a system of programs called the POLYATOM system, which allows one to specify the types of atoms and their positions in a polyatomic molecule, and which then proceeds to compute the various molecular integrals required for solving the quantum-mechanical problem of the electronic structure of this molecule, to combine these integrals in a suitable way, and to end up with a calculation of the electronic wave function. Applications of early versions of this method to the structure of benzene and of ethylene are described, and examples of more complicated molecules which have been discussed by the method are described.