Summary: A number of authors have previously used group representation theory to block-diagonalise the stiffness matrix of a symmetric structure. This paper describes how similar techniques can be used to block-diagonalise the equilibrium matrix of a symmetric structure. This is shown to provide useful insight into static and kinematic response of such systems. In particular, it simplifies the classification of states of self-stress and mechanisms, as well as reduces computational effort required for the force method analysis.