Abstract: The acoustic radiation modes constitute a set of independent basis functions defined on the vibrating surface and describe the radiation patterns of multi-pole. The field distribution modes constitute a set of independent basis functions defined on the radiation field and describe the distribution patterns of multi-pole radiation. The radiation from the vibrating surface can be uniquely expressed in terms of the acoustic radiation modes or the field distribution modes. For econstruction of acoustic fields, the key is to determine the expansion coefficients. At N measurement points in the acoustic field, measuring the acoustic information, the expansion coefficients can be determined and the total acoustic field can be reconstructed. For the radiation of a plate and a sphere, the acoustic fields are reconstructed, and the numeral calculation results agree with the theoretic results