In this paper, the problem of the navigation error effect for the optimal and constraint Trajectory of the UAVs that are required to fly at low altitude over terrains has been discussed. Due to the increasing deviation problem of inertial navigation systems in terms of time, having a safe flight and collision avoidance with terrain at low altitude is the main point in the trajectory design of this type of the vehicles. On the other hand, some of these vehicles use Terrain Contour Matching (TERCOM) as a navigation aiding system. This system is more efficient in rough terrains, and providing the requirements of this system beside other constraints is a complex task. In this paper is tried to meet these constraints in the trajectory design process. For this purpose, an algorithm based on the layered network flow on the digital terrain maps used in a manner that has a high potential in adoption of various constraints and optimal trajectory is generated. Then, using equations of motion on a terrain digital data in 3D space with the dynamical constraints and different optimality criteria, a complete model of navigation error and also parameters affecting TERCOM has been developed to generate feasible path reducing terrain collision probability to zero.. Numerical results show validity of this issue.