This paper explores low observability flight path planning of unmanned air vehicles (UAVs) in the presence of radar detection systems. The probability of detection model of an aircraft near an opponent radar depends on aircraft attitude, range, and configuration. A detection model is coupled with a simplified aircraft dynamics model. The nonlinear trajectory generation (NTG) software package developed at Caltech is used. The NTG algorithm is a gradient descent optimization method that combines three technologies: B-splines, output space collocation and nonlinear optimization tools. Implementations are formulated with temporal constraints that allow periods of high observability interspersed with periods of low observability. This feature can be used strategically to aid in avoiding detection by an opponent. Illustrative examples of optimized routes for low observability are presented.