This work presents an accurate way for calculating partition functions of strongly coupled hindered rotors in two dimensions. The two-dimensional torsional potential is generated from electronic structure calculations and fitted to Fourier series. The kinetic energy includes off-diagonal terms which are allowed to vary with the torsional angles, and these terms were also fitted to Fourier series. The resulting Hamiltonian leads to a coupled Schrödinger equation which was solved by the variational method. Therefore, the final two-dimensional non-separable (2D-NS) partition function incorporates coupling terms in both the kinetic and the potential energy. The methodology has been tested for propane, methyl formate, and a hydrogen abstraction transition state from propanone by the OH radical. How to incorporate the 2D-NS partition function in the total vibrational-rotational partition function is also discussed.