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In the adaptation of nonconforming finite element methods to the equations of elasticity with traction boundary conditions, the main difficulty in the analysis is to prove that an appropriate discrete version of Korn's second inequality is valid. Such a result is shown to hold for nonconforming piecewise quadratic and cubic finite elements and to be false for nonconforming piecewise linears. Optimal-order error estimates, uniform for Poisson ratio i^6[0, 1/2), are then derived for thedoi:10.1090/s0025-5718-1991-1094947-6 fatcat:dupfnk262zfmza3yije6lgmh6y