Abstract: The nonparametric detection methods for radar target are extensively used in radar system, due to the fact that they can ensure Constant False Alarm Rate (CFAR) for a wide class of input noise distributions and can be easily implemented. In this paper, the detection performance of the Rank Sum (RS) nonparametric detector is investigated analytically for homogeneous background and multiple targets situation, with an assumption of Weibull distributed clutter, for a Swerling II targets model. The mathematical models of detection probability for the RS detector in homogeneous background and multiple targets situation under Weibull assumption are derived. The obtained results show some theoretical and practical values for the design of a radar target detector.