When in-flight failures occur, rapid and precise decision-making under imprecise information is required in order to regain and maintain control of the aircraft. To achieve planned aircraft trajectory and complete landing safely, the uncertainties in vehicle parameters of the damaged aircraft need to be learned and incorporated at the level of motion planning. Uncertainty is a very important concern in recovery of damaged aircraft since it can cause false diagnosis and prognosis that may lead to further performance degradation and mission failure. The mathematical and statistical approaches to analyzing uncertainty are first presented. The damaged aircraft is simulated via a simplified kinematics model. The different sources and perspectives of uncertainties under a damage assessment process and post-failure trajectory planning are presented and classified. The decision-making process for an emergency motion planning to landing site is developed via the Dempster-Shafer evidence theory. The objective of the trajectory planning is to arrive at a target position while maximizing the safety of the aircraft under uncertain conditions. Simulations are presented for an emergency motion planning and landing that takes into account aircraft dynamics, path complexity, distance to landing site, runway characteristics, and subjective human decision.