A quasi-analytical method for the solution of direct eddy current testing problems for the case of cylindrical volumetric flaws is presented in the paper. The method is based on a simple physical assumption that the electromagnetic field induced by a coil carrying alternating current is exactly equal to zero at a sufficiently large radial distance from the coil. The axis of the coil concides with the axis of a cylindrical flaw. The method of truncated eigenfunction expansions is used to compute the change in impedance of the coil. Complex eigenvalues are computed numerically using the method which does not require initial approximation for the eigenvalue. Computations are presented for different values of the parameters of the problem. Calculated change in impedance is compared with numerical results obtained by means of Comsol Multiphysics software. Good agreement between quasi-analytical method and numerical solution is found.