In the context of mechanical system modelling using bond graph language, this paper proposes a procedure consisting of a systematic bond graph causality assignment and the analytical exploitation of the causal bond graph obtained. The equations issuing from this analytical exploitation are the Lagrange equations using the $\lambda$-multiplier method. The set of DAE (Differential-Algebraic Equations) implicit Lagrange and kinematical equations are obtained by expressing an effort balance at the ``generalized 1-junctions" and a flow balance at the ``constraint 0-junctions". The specialist can work with his own preferred form of equations (namely the Lagrange equations) and the non-specialist can manipulate high domain dependent analyses with a relative simple graphic concept (namely the bond graph). Moreover, due to the pluridisciplinary feature of bond graph language, the Lagrange equations, using the $\lambda$-multiplier method, can be used for different physical domains. The paper is organized as follows : an introduction traces an overview of existing procedures for obtaining the Lagrange equations from a bond graph representation (Karnopp 1977; van Dijk 1994). The first part presents the procedure proposed in this paper. The second part details the application of this procedure to the example of a crank-slider mechanism. The third part explains the important issues of this procedure. Finally the conclusion draws some perspectives.