This paper numerically investigates the tilt response of multi-storey buildings due to progressive collapse of the adjacent underground structure under internal blast loading. The software LS-DYNA is utilized to establish a three-dimensional coupled model composed of the underground structure, the soil around and the adjacent above-ground structure. In order to reduce the computational cost, an efficient computational method, Three-Stage Simulation Method (TSSM), is put forward. Three different methods, Alternative Path Load Method (APLM), Direct Simulation Method (DSM) and TSSM, are used to analyze the same model which illustrates the correctness of the model and the proposed method. By comparing tilt response of the above-ground structure of different types due to progressive collapse of underground structure under its internal blast loading, it is found that the tilt response of the above-ground structure of different types is related to the foundation of the structure. For example, compared with the frame structure with basement, the frame-shear wall structure with basement can prevent structure from great tilt response. However, the tilt response of the frame-shear wall structure with raft basis is larger than that of the frame.