Stacking a few layers of 2D materials such as graphene or molybdenum disulfide at controlled twist angle has opened the possibility of tuning the electronic properties of 2D materials. One of the main issues encountered in the mathematical and computational modeling of twisted 2D materials is that lattice mismatch and rotations between the layers destroys the periodic character of the system. We have developed a novel variational model for elastic relaxation and a new mathematical formulation for the electronic density of states, band structure, and transport for the incommensurate Hamiltonian. New computational approaches will be presented, and the validity and efficiency of these approximations will be examined from mathematical and numerical analysis perspectives.