The effect of irradiation on the microstructure of metals often produces a high number density of dislocation loops, consisting of self-interstitial platelets. In dislocation theory these damage clusters are treated as prismatic dislocation loops. The elastic fields of such loops are solved analytically in the literature typically for loops in an infinite material. Near a free surface this solution is altered by image stresses. This work presents an analytically derived solution for the elastic fields of a sub-surface rectangular dislocation loop in a half material. Resulting surface displacements are compared against Molecular Dynamics (MD) computations for Tungsten.