Magneto-sensitive (MS) or magnetorheological (MR) elastomers are smart materials whose mechanical properties change instantly by the application of a magnetic field. MS elastomers are widely used in the practice as elements of MEMS (sensors, actuators, etc.), for example, in medical devices. The behavior of MS elastomers under time-dependent magnetic field is a complex process and till now is not investigated in all details. Here we present the statements of the dynamic boundary-value problem of a MS elastomer and demonstrate the special features of the dynamic behavior of such system. As an example both the nonlinear and the linear oscillations of a MS elastic sphere are considered. The control of radially symmetric oscillations of MS elastic sphere by a homogeneous magnetic field is investigated. The presented results can be used for control and generation of radially symmetric acoustic waves using magnetic field excitation.