The aim of this work is to compare different marking strategies, their influence on the work of adaptive algorithms with a posteriori error control for plane elasticity problems. The error control was performed using functional error majorant. Implemented adaptive algorithms were based on the functional error majorant with no symmetry limitation on free tensor, computed using the zero-order Raviart-Thomas approximations on triangular meshes. The four most commonly used element marking criteria were used in adaptation. Numerical results for several plane strain problems have been presented, including the case of different materials and geometry. A comprehensive analysis of obtained results was given.