With the discovery of graphene in 2004, experiments have quickly confirmed that many of its low energy properties are well-described by a Dirac Hamiltonian for massless fermions. This has created intense interest in other Dirac-like materials and model Hamiltonians. In this thesis, we compute the electronic density of states and optical conductivity for a semi-Dirac model in three dimensions. This model is Dirac-like in two of the dimensions and free-electron-like in the third, generalizing the two-dimensional semi-Dirac Hamiltonian to three dimensions. We find different power-law behaviour in the frequency-dependent conductivity in different directions, which would provide a signature of the Hamiltonian if seen in experiments. We also provide an analytic form for the conductivity in a more general case and contrast our results with other models in the literature, for example, graphene, three-dimensional Weyl, and the two-dimensional semi-Dirac.