Abstract: Boundary value problems for dynamical systems with periodicsolutions can be turned into initial value problems. With this point inmind, the paper improves the shooting method. In the process ofcomputing derivatives of boundary conditions' algebraic equations, which arefunctions of unknown initial value parameters, the node function values areobtained through Runge-Kutta method, and by using Runge-Kutta methodonce more, the derivatives can be obtained. The validity of such a method isverified by using it to obtain periodic solutions of Duffing equation andnolinear rotor-bear system, and comparing the results with those computed bytraditional method. Meanwhile, we discuss the stability of the solutions byFloquet theory.