The dynamics of a Flexible Manipulator system are described by an infinite-dimensional mathematical model, since the model consists of partial differential equations. But to design a finite-dimensional controller, a finite-dimensional system model is needed. To achieve this goal, a finite dimensional approximation needs to be used to model a flexible manipulator, that is, to retain a finite number of modes, and to drop off the other, less significant modes based on the requirements of the controller. The scheme in developing a mathematical model is to use the Lagrangian method or Hamiltonian’s Principle to the total kinetic energy, total potential energy and virtual work done by the torque actuated to the joint. This method will not introduce extra errors into system and will be used to obtain the state-space model for a flexible manipulator suggested in this paper. Dynamics of flexible manipulators with shear force and rotatory inertia are derived, and state-space equations with the integration of DC motor dynamics are developed as a theoretical base for mechatronic designs.