Dolphins use their biosonar to discriminate objects with different features through the returning echoes. Cross-modal matching experiments were conducted with a resident bottlenose dolphin (Tursiops aduncus). Four types of objects composed of different materials (water-filled PVC pipes, air-filled PVC pipes, foam ball arrays, and PVC pipes wrapped in closed-cell foam) were used in the experiments, respectively. The size and position of the objects remained the same in each case. The data collected in the experiment showed that the dolphin's matching accuracy was significantly different across the cases. To gain insight into the underlying mechanism in the experiments, we used finite element methods to construct two-dimensional target detection models of an echolocating dolphin in the vertical plane, based on computed tomography scan data. The acoustic processes of the click's interaction with the objects and the surrounding media in the four cases were simulated and compared. The simulation results provide some possible explanations for why the dolphin performed differently when discriminating the objects that only differed in material composition in the previous matching experiments.