Abstract: A multi-variate functionalПRSis derived from plate functionalПRPby relaxing the constraint between shear strain, rotation and deflection, with shear force introduced as a variate. Then, by tensorial interpolation formulation, the shear strain field can be derived. Making use of the invariance property of tensor, disadvantages due to coordinate transformation are avoided, thus helpful to identify the zero energy modes. By expressing the shear strain in tensorial form, proper selection of optimal shear force interpolating function is successfully achieved on the basis of“one stress parameter per one deformation mode”. Thus, an efficient free shear locking 4-node hybrid/mixed plate element is constructed. Numerical examination reveals remarkable characteristics of Prs against the existing counterparts.