Numerical analysis methods including finite element analysis (FEA), computational fluid dynamics (CFD), and fluid-structure interaction (FSI) analysis have been used to study the biomechanics of human tissues and organs, as well as tissue-medical device interactions, and treatment strategies. However, for patient-specific computational analysis, complex procedures are usually required to set-up the models, and long computing time is needed to perform the simulation, preventing fast feedback to clinicians in time-sensitive clinical applications. In this study, by using machine learning techniques, we developed deep neural networks (DNNs) to directly estimate the steady-state distributions of pressure and flow velocity inside the thoracic aorta. After training on hemodynamic data from CFD simulations, the DNNs take as input a shape of the aorta and directly output the hemodynamic distributions in one second. The trained DNNs are capable of predicting the velocity magnitude field with an average error of 1.9608% and the pressure field with an average error of 1.4269%. This study demonstrates the feasibility and great potential of using DNNs as a fast and accurate surrogate model for hemodynamic analysis of large blood vessels.