A method combining boundary and finite element approaches as well as modal analysis to solve the acoustical scattering from elastic obstacle in infinite fluid is described. An elastic cylinder with finite length immersed in water is chosen as an example for numerical demonstration. The computed frequency response and direction pattern of the backscattering target strength of the cylinder are conformable to those measured. A method combining boundary and finite element approaches as well as modal analysis to solve the acoustical scattering from elastic obstacle in infinite fluid is described. An elastic cylinder with finite length immersed in water is chosen as an example for numerical demonstration. The computed frequency response and direction pattern of the backscattering target strength of the cylinder are conformable to those measured.