Seismic refraction tomography is one of the imaging techniques in geophysical methods used to remodel the near-surface velocity layer structure of the Earth. In this study, we carried out a new computational approach and modelling of seismic refraction tomography using the pseudo-bending method. The true model of the near-surface is designed to be anisotropic medium which is having a low velocity anomaly distribution. This anomaly is constructed in such a way as to be similar to a model of liquid waste away spreading, which exhibits seismic velocities ranging from 1600 m/s to 1800 m/s. Based on our computations and numerical modelling results, it was found that the ray tracing path using pseudo-bending method displays an asymmetrical trajectory when the positions of the source and geophone are exchanged. Altering the shooting configuration from direct shoot (DS) to reversed shoot (RS) also reveals a significant difference in travel time values. The results of delay time tomography inversion, which represents the difference between travel times in the true model and the initial model using the SIRT method, indicate the presence of a low velocity anomaly that can be interpreted as the distribution of liquid waste.