The static deformation problem of a transversely isotropic and layered half-space by general dislocation sources is solved. The solution is given in the Cartesian system and the cylindrical system of vector functions using multiplications of matrices. The source functions of general dislocations in a transversely isotropic medium are obtained in these two systems using a new approach. Explicit expressions for the surface displacements due to three- and two-dimensional dislocation sources are also obtained in terms of the cylindrical system and the Cartesian system of vector functions, respectively. It is shown that the present solution contains the solutions to the three- and two-dimensional source problems for the corresponding isotropic media, and therefore provides a unified solution for these two problems, which have long been studied separately. The formulation developed can be evaluated numerically to study the effects of anisotropy, as well as of Earth layering, on the static fields.