Homogeneous elastic media subjected to two types of field sources: body forces (external sources) and dislocations (internal sources) are considered. The strain and stress fields caused by these sources are presented in the integral forms using Green’s function of the system of the governing equations of elasticity. Relations of the integral operators in these presentations with the projectors on the divergence-free and rot-free tensor subspaces are revealed. Discontinuities of the elastic fields in the medium subjected to the stress sources are studied. For presentations of elastic fields far from the sources, the concept of multipole expansions of the source densities is introduced.