We describe in this paper the Cuckoo Search Algorithm via Lévy flights and present the study of parameters behavior in the algorithm. CS is a stochastic algorithm, inspired by the natural behavior of a family of birds called Cuckoos. The parameters considered in the study are: Pa (probability to be discovered by the host bird), α (is the step size), b (variable included in Lévy distribution). The experiments were performed with the Rosenbrock function. We will observe the behavior of Pa, α and b parameters according to the variation of their rank, the number of iterations and the effect they have on the optimal value.