Abstract In modern seismology, dislocation theory plays an important role in the computation of surface deformation induced by an internal dislocation source. Many researchers have studied quasi-static dislocation theory; however, their works are built on the basic solution of deformation equations given by the classic literature. In this paper, we first review the physical equations of dislocation theory, including the equilibrium equation, constitutive relation, and Poisson’s equation. Then we solve these equations under the non-gravitating, incompressible, and compressible gravitating homogeneous earth model, giving their general solutions including the spheroid and toroid components. The basic solutions under a homogeneous sphere given in this paper can be used to improve understanding and computation of seismic deformations under a layered spherical earth.