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In this paper, a semi-analytical approach for the 1 eigenproblem of circular plates with multiple circular holes is 2 presented. Natural frequencies and modes are determined by 3 employing the null-field integral formulation in conjunction 4 with degenerate kernels, tensor rotation and Fourier series. In 5 the proposed approach, all kernel functions are expanded into 6 degenerate (separable) forms and all boundary densities are 7 represented by using Fourier series. By uniformly collocating 8 points on the real boundary and taking finite terms of Fourier 9 series, a linear algebraic system can be constructed. The 10 direct searching approach is adopted to determine the natural 11 frequency through the singular value decomposition (SVD). 12 After determining the unknown Fourier coefficients, the cor13 responding mode shape is obtained by using the boundary 14 integral equations for domain points. The result of the annular 15 plate, as a special case, is compared with the analytical solu16 tion to verify the validity of the present method. For the cases 17 of circular plates with an eccentric hole or multiple circu18 lar holes, eigensolutions obtained by the present method are 19 compared well with those of the existing approximate analyt20 ical method or finite element method (ABAQUS). Besides, 21 the effect of eccentricity of the hole on the natural frequency 22 and mode is also considered. Moreover, the inherent prob23 lem of spurious eigenvalue using the integral formulation is 24 investigated and the SVD updating technique is adopted to 25 suppress the occurrence of spurious eigenvalues. Excellent 26 accuracy, fast rate of convergence and high computational 27 W. M. Lee Department of Mechanical Engineering, China Institute of Technology, Taipei, Taiwan J. T. Chen (B) Department of Harbor and River Engineering, National Taiwan Ocean University, P.O. Box 7-59, Keelung 20224, Taiwan e-mail: [email protected] efficiency are the main features of the present method thanks 28 to the semi-analytical procedure. 29