Lung mass density is directly associated with lung pathology. Computed Tomography (CT) evaluates lung pathology using the Hounsfield unit (HU) but not lung density directly. We have developed a lung ultrasound surface wave elastography (LUSWE) technique to measure the surface wave speed of superficial lung tissue. The objective of this study was to develop a method for analyzing lung mass density of superficial lung tissue using a deep neural network (DNN) and synthetic data of wave speed measurements with LUSWE. The synthetic training dataset of surface wave speed, excitation frequency, lung mass density, and viscoelasticity from LUSWE (788,000 in total) was used to train the DNN model. The DNN was composed of 3 hidden layers of 1024 neurons for each layer and trained for 10epochs with a batch size of 4096 and a learning rate of 0.001 with three types of optimizers. The test dataset (4000) of wave speeds at three excitation frequencies (100, 150, and 200Hz) and shear elasticity of superficial lung tissue was used to predict the lung density and evaluate its accuracy compared with predefined lung mass densities. This technique was then validated on a sponge phantom experiment. The obtained results showed that predictions matched well with test dataset (validation accuracy is 0.992) and experimental data in the sponge phantom experiment. This method may be useful to analyze lung mass density by using the DNN model together with the surface wave speed and lung stiffness measurements.