Recent advancements and progress in engineering have driven increasing demands for better performance and reliability in aerospace systems. To meet these demands, designers conduct design and optimization studies considering all aspects of the life cycle phase from initial design to final disposal. Throughout the life cycle of a real-world product, countless inherent uncertainties arise from both the system itself and the environmental and operational conditions under which it operates. Specifically, in aerospace systems, uncertainties may originate from manufacturing resources, material properties, model approximations, loading conditions applied to the structure, and operating conditions. These uncertainties can lead to variations in system performance, significant deviations, and potentially severe malfunctions or mission failures. Uncertainty Quantification (UQ) plays a pivotal role in addressing these inherent uncertainties in aerospace systems, ensuring that performance, safety, and reliability standards are maintained across the entire life cycle. Given the complexity of aerospace systems and the vast number of uncertainty sources, UQ often requires evaluating numerous candidates to explore the full spectrum of potential behaviors and outcomes. This process can be computationally expensive, especially when relying on high-fidelity CFD/FE simulations. To tackle this challenge, surrogate models are often employed to approximate the system's response to different uncertainty scenarios. Specifically, while widely used to reduce the cost of UQ studies, traditional surrogate models struggle to efficiently capture the underlying physics and uncertainties for especially high-dimensional systems. Multi-fidelity analysis methods are mostly utilized to diminish the computational burden of high-fidelity simulations. In this work, the multi-fidelity deep neural network (MFDNN) proposed by Meng et al. will be employed. The study aims to demonstrate the effectiveness of MFDNNs on the UQ studies tailored for both analytical benchmark functions and high-dimensional aerospace engineering design problems. We first validate the MFDNN-based UQ framework with analytical functions. Then, we will perform UQ studies for aerodynamic and aeroelastic design problems, and investigate the efficiency of the MFDNN methods on especially high-dimensional cases. The obtained results will be compared with traditional surrogate models in terms of accuracy and computational time.