The authors present a concept of constructing the equations of motion for a single-bucket pulling excavator in terms of generalised Lagrange's variables. The applied model is based on the assumption that the excavator is a system of rigid solids connected with rotational constrains of ten degrees of freedom. The essence of the proposed algorithm consists in reducing the procedure of constructing the system of excavator's motion equations to multiplication of adequate matrices. One avoids analytical or numerical derivation of the consecutive time derivatives of kinetic and potential energy of the system. The algorithm formulated in such a way may constitute a basis for constructing a numerical program for the analysis of excavator system dynamics. The proposed method of generation of Lagrange's equations can be generalised and applied to a wider class of multibody systems.