Abstract: The implicit algorithm of multibody systems with topological tree configuration is studied. The canonical equations of the system and the general form of Jacobian matrix of the equations are obtained in the form of matrix. The paper presents the algorithm of Jacobian matrix divided into several submatrices and the diagonal implicit Runge-Kutta method( DIRKM) and implicit symplectic Runge-Kutta method (ISRKM) of canonical equations of the multibody system. The methods are suitab...