This paper presents a numerical analysis on the structural and acoustic behaviours of a stiffened composite cylindrical shell containing piecewise isolators. The system is immersed in an unbounded, compressible and inviscid fluid. The composite cylindrical shell is reinforced by a series of circumferential rings and longitudinal stringers, which may be few or many in number, non-uniform or uniform in size, and non-uniformly or uniformly spaced, are treated as discrete elements. The isolators in the cylindrical shell contain motion-limiting stops, the restoring forces of which are expressed as bi-linear functions of the isolator deformation. The nonlinear dynamics model of the structural system is established by using a modified variational method, and the acoustic fluid is modelled by a time-domain boundary element method. Physical insight into mechanism of the nonlinear vibration and radiated sound responses of the coupled structural system is provided.