  We study the linear elasticity system subject to singular forces. We show
existence and uniqueness of solutions in two frameworks: weighted Sobolev
spaces, where the weight belongs to the Muckenhoupt class $A_2$; and standard
Sobolev spaces where the integrability index is less than $d/(d-1)$; $d$ is the
spatial dimension. We propose a standard finite element scheme and provide
optimal error estimates in the $\mathbf{L}^2$--norm. By proving well posedness,
we clarify some issues concerning the study of generalized mixed problems in
Banach spaces.
