This dissertation explores optimal path planning techniques for safe navigation of autonomous air vehicles. Finding trajectories for multiple vehicles moving in a dynamic environment while satisfying all constraints is a challenging problem. No single technique can be used independently for this problem. Different techniques for real time path planning have been developed and compared. First the problem was addressed using optimal control theory. Equations governing necessary conditions were derived for a combined objective of terrain avoidance, radar avoidance and minimum path length. Using these equations, analytical solutions for radar risk minimization problem have been derived. A gradient method was used to get an optimal solution for different radar geometries. Mixed integer linear programming (MILP) formulation employing branch and bound techniques was investigated for both single and multiple autonomous air vehicle trajectory planning. A novel real-time receding horizon approach using MILP has been proposed that uses binary variables to model the soft and hard constraints for radar zones. A three dimensional probabilistic approach for the path planning unmanned air vehicles(UAVs) has been considered as well. For this approach a probabilistic cost function has been developed that accounts the various factors of fuel, collision, crash to ground objects etc. The novelty of the algorithm relies in its ability to be used in real time due to very low computational load in spite of the fact that it finds a path in three dimensions. The paths are locally optimal and are feasible for the UAV to follow. For graph-based global optimality, a software has been developed that includes extra subroutines to modify the already implemented Voronoi code in order to remove the infinity and far away nodes and also includes the corner points of the operational area. This software has been employed to find the Length Constraint Least Risk (LCLR) paths and also different techniques were compared.