Abstract: In this paper,it is proved that the well-known Hu-Washizu variational principle is a pseudo- generalized variational principle(pseudo-GVP),which is a functional whose stationary conditions would satisfy all its field equations and boundary conditions if all the variables in the functional were considered as independent variations,but in fact there might exist some kinds of constraints.Some new pseudo-GVPs are established to distinguish them from genuine ones by the so-called inverse Lagrange multiplier method.The constrained Hu-Washizu principle,therefore,is proved to be equivalent with the Hellinger-Reissner principle under the same constraints of stress-strain relations.