The applicability of the field-consistency paradigm, which was originally employed for analysis of locking due to constrained energy having the second power of a strain, is extended to the constrained energy having a quadratic form of strain. For the extension, nearly-incompressible plane strain problem is considered by introducing the concept of reduced minimization. The field-consistent analysis of the plane strain problem leads to a clear and systematic understanding on the relation amongst constraints imposed on element, spurious constraint -free optimal points, and integration order used.