The paper deals with methods and procedures for automatic generation of dynamical equations of multibody systems by means a Maple package called 'MBSymba'. The authors give a brief survey of the current state in the field of multibody systems modeling. As a case study, a model of a motorcycle (model of four rigid bodies with the five degrees of freedom) is considered. The first step in modeling of a multibody system is the description of its initial objects (such as points, vectors, rigid bodies, forces and torques) and relationships between them, including some additional variables and equations, which may define the control or another object subsystems. All classical methods for deriving equations of motion can be codified by standard sequence of operations. The authors describe a set of commands for deriving second-order Lagrange's equations. The possibilities of package procedures for linearizing and manipulating equations are illustrated by considering the stability, control design or optimization. All described package procedures are designed for generating C or Fortran codes for numerical simulations.