Stability of the internal tilting mode in an elongated prolate field-reversed configuration (FRC) is investigated numerically. Eigenfrequencies are calculated from a Vlasov-fluid dispersion functional that is separated into fluid and kinetic portions. The latter are evaluated by a Monte Carlo method following a sample of the equilibrium orbits. An innovative Fourier transform technique is developed to reduce the operation count of the algorithm. Kinetic growth rates obtained for an experimentally relevant equilibrium indicate essential stabilization of internal tilting in an FRC with s̄≲2, where s̄ measures the number of thermal gyroradii in the configuration. For s̄→∞ the kinetic growth rates approach previous magnetohydrodynamic (MHD) values.