Summary: A new theory is presented for the generation of two-dimensional internal wave beams, including the effects of viscosity and unsteadiness on the propagation of the waves, and extending to the near field the classical theory of Lighthill for the far field. For this, the forcing is assumed to be of compact support. Several equivalent expressions of the waves are obtained, each associated with the choice of a support of simple shape embedding the actual support of the forcing. When the two match, the expression of the waves is valid everywhere in the fluid. For an oscillating body, the existence of critical points where the waves rays are tangential to the body is correctly accounted for, an essential requirement with regard to later inclusion of nonlinear effects and boundary layer eruption into the analysis, both of which take their origin at the critical points. Embedding supports in the shape of a circle, an ellipse and a strip are considered. Line forcing is also considered, on a weaker assumption of rapid decrease at infinity. The analysis reduces to the classical analysis of Hurley & Keady in the isotropic case of an oscillating circular cylinder, and is otherwise applied to four anisotropic oscillating bodies: an elliptic cylinder, a vertical plate, a vertical wave generator and a thin Gaussian bump.