Adaptive solutions have so farreceived considerable attention due to the need of obtaining a certain level of accuracy in finite element method. The basic concept in such solutions is computation of the error of the approximation. From two categories of the error estimations, i.e. the residual and the recovery based error estimation, the latter, proven by the pioneering researches to be superior to the former, has been addressed in this research. Application of two recently developed recovery methods i.e. Superconvergent Patch Recovery (SPR) and Recovery by Equilibrium of Patches (REP) to the problems of thick plates using Mindlin-Reier formulation has been studied here. The basis of these two recovery methods is smoothing the stress components on a patch of elements. In the first method especial sampling points, termed as superconvergent points, are needed, however, the second one dose not require any knowledge of such points and thus has a wider range of application (i.e. nonlinear problems of elasto- plasticity etc.) Comparison of the performances of the two methods for plane strain/stress problems can be found in the litrerature. Here the comparison is made on a benchmark problem using regular meshes of quadrilateral and triangular plate elements for both linear and quadratic approximations. The results of this research show that same as for two-dimentional problems is also valid for the plate problems and both methods perform equally well. In order to investigate the possibility of any improvement by applying some equilibrume constraints, as some researches suggest, various forms of such constrains have been devised and applied to the problem. The studies show that although the restrained forms are rather expensive due to the coupling effect in the constraint expressions, insignificant improvement is obtained when the results are compared to those of the original forms