If the elastic coefficients are not constant throughout the whole body, such materials are called inhomogeneous. In this paper, using the concept of the parametrix of the fundamental equations in elasticity, the classical main results in the theory of elastic potentials developed by Fredholm, Weyl, Kupradze and many others have been extended to the case of inhomogeneous materials. Here, by the parametrix of the three dimensional elasticity, we mean the 3×3 square matrix constructed by the nine functions [numerical formula] where, λ and μ are Lame's coefficients, x and y are the points in the elastic body, and δ_s^k is Kronecker's delta. Finally in this paper, the reduction of the fundamental boundary value problems in elasticity to Fredholm systems of singular integral equations is considered.