Summary: Hybrid stress-based finite elements with side displacement fields have been used to generate equilibrium models having the property of equilibrium in a strong form. This paper establishes the static and kinematic characteristics of a flat triangular hybrid equilibrium element with both membrane and plate bending actions of general polynomial degree \(p\). The principal characteristics concern the existence of hyperstatic stress fields and spurious kinematic modes. The former are shown to exist for \(p > 3\), and their significance to finite element analysis is reviewed. Knowledge of the latter is crucial to the determination of the stability of a mesh of triangular elements, and to the choice of procedure adopted for the solution of the system of equations. Both types of characteristic are dependent on \(p\), and are established as regards their numbers and general algebraic forms. Graphical illustrations of these forms are included in the paper.