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This paper forms the second part of a two-part paper on the evaluation of local a posteriori error estimation for FEM. The first part provided an assessment of the error estimators to stead-state flow problems, whereas this second part deals with elasticity problems. Problem formulation presented in Part I is extended to account for the coupled displacement field appearing in elasticity problems. The two error estimators, the element residual method (ERM) and Zienkiewicz-Zhu patch recovery technique (ZZ) are used as drivers for a mesh adaptation process. The results demonstrate the advantages of employing a posteriori error estimators for obtaining finite element solutions with a pre-specified error tolerance. Of the two methods, the ERM is shown to produce adapted meshes that are similar to those adapted by the exact error. Furthermore, the ERM provides higher quality estimates of the error in the global energy norm when compared to the ZZ estimator.