A continuum can be controlled by a small number of sensors and actuators without causing observation and control spillover. The time response is determined by solving integral equations with respect to only the joint displacements of member beams. The integral equations can be solved with little computation time by transforming them into ordinary differential equations and by introducing additional mass corresponding to the inertial force due to the rigid-body axial translation and rotation of member beams. The proposed method is advantageous with regard to precision, computation time and resolution of the spillover problem compared with conventional methods resorting to FEM. Numerical examples deal with the control of the position, attitude and elastic deformation of a space structure and a manipulator arm, a vehicle frame supported by nonlinear springs and a truss with a dynamic absorber used for economizing the energy consumed for the active control.