The dynamic Young’s modulus and loss factor of a viscoelastic material may be calculated as functions of frequency from data on the relative motions of the two ends of a bar of the material that is in harmonic oscillation at that frequency. Most investigators using this technique have confined their measurements to resonant frequencies, but it would be useful to find the moduli of the material at regular, narrowly spaced intervals of frequency. The characteristic equation, from which the moduli of the material are calculated, is investigated with respect to numerical solvability and stability. It is shown that this equation has infinitely many solutions. An apparently effective method of choosing the physically relevant solution is developed. It is found in the case of low‐loss materials that at certain frequencies solutions to the characteristic equation lie near zeros of the Jacobian, which are the solutions in the limiting case of a perfectly elastic material. Consequently, low‐loss viscoelastic materials will exhibit great sensitivity to errors in measurement at these frequencies. An error analysis is developed in order to estimate the magnitude of this instability. A microcomputer program written to solve these equations is applied to various simulated samples to illustrate the effects of this instability.