A purely bending model considering the clearance, stiffness, damping of joints and nonlinear cables, is derived to show the nonlinear dynamic characteristics of jointed deployable structures. The Taylor series expansion of nonlinear differential equation and harmonic expansion of variables are used to convert the nonlinear dynamic equation to nonlinear algebraic one. The response of the deployable structures can be analyzed by iteration method. The numerical analysis by Runge-Kutta method for deployable structures is employed to validate the incremental harmonic balance (IHB) method. IHB method is used to analyze the stability of response for deployable structures when the exciting frequency changes, which is based on the nonlinear dynamic model. The stability of deployable structure response are presented in a frequency range when the clearance and stiffness of joint, exciting force and cable change. The IHB method can be used for multi-degree deployable structures to obtain the steady response and nonlinear dynamic characteristics, which provides a method for further research of the dynamics of jointed deployable structures.