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As for the acoustic radiation calculation of vibrating structures in the free field, less attention has been paid to the time domain analysis than frequency domain analysis. Nevertheless time domain sound calculation is essential for applications in which the dynamic process should be carefully addressed. Previous researchers tried hard to improve the efficiency of transient acoustic radiation calculation and have made many progresses. However, until now the transient acoustic radiation in the free field still suffers from insufficient computational resources and low efficiency when the number of discrete elements is large and the temporal sample sequence is long. In order to solve these problems, a modal expansion and spatial delay based transient sound field calculation method is proposed. By constructing the DMATM (Delayed Modal Acoustic Transfer Matrix) in the proposed method, the physical coordinates of structural nodes are transferred to lowdimensional modal coordinates and the spatial delay information of different nodes is preserved. To describe this method in detail, the acoustic radiation process of the impact sound synthesis of a cylinder is investigated. The results show that the proposed method is more efficient than previous methods under the same accuracy.