Semi-analytical solutions of eddy current testing problems require several computational steps. One of the steps where numerical methods are needed is calculation of complex eigenvalues without good initial approximation for the roots. In the presented paper we describe three eddy current testing problems with cylindrical symmetry where a cylindrical inclusion in a conducting medium is of finite size. In all three cases eigenvalue problem reduces to transcendental equations containing Bessel functions in a complex plane. The algorithm of the solution of such problems is described in the paper. Results of numerical computation are presented.