Several methods have been developed in the literatures of computational mechanics to improve the performance of the conventional lower-order displacement finite elements which yield poor results for problems with bending and for nearly incompressible medium. This paper is devoted to a unified analysis of convergence for Pian–Sumiharas, Chen-Cheungs and Piltner-Taylor s enhanced stress/strain schemes. By virtue of the energy compatibility and the rank condition, error estimates for these typical finite elements of high prformance are obtained in a unified framework, and especially, weakly locking-free error estimates with respect to the Poisson s ratio m in energy norms are obtained uniformly for v ≤ (1-Ch) =2 as h → 0, where C is a constant independent of m and the mesh size h. Very much the same about the three methods is pointed out.