Power reactor noise, which describes the fluctuations of the neutron flux around its mean value, is a valuable tool in nuclear reactor monitoring. In recent years, several numerical tools have been developed to solve the Fourier-transformed Boltzmann equation that underpins neutron noise theory in the frequency domains. Among the proposed computational strategies, Monte Carlo methods are motivated by the need to perform high-fidelity simulations of the neutron noise field.The numerical treatment of the noise equations usually relies on the “orthodox” linearization, a first-order approach that consists of neglecting the product of the perturbed quantities. This approximation is known to fail for the higher-order harmonics of the noise fields induced by mechanical vibrations, a case of interest in real-world applications.In view of these considerations, in this work we propose a strategy to directly solve the noise equation in the frequency domain using a nonperturbative approach, i.e. without resorting to linearization. This strategy is naturally suited to Monte Carlo methods, but also extends to deterministic approaches. We present the general theory and the full implementation; furthermore, a proof of concept is carried out on a few relevant benchmark configurations, along with parametric studies and performance analysis.In the investigated applications, the nonperturbative Monte Carlo algorithm is shown to be both more accurate and efficient than its linear theory counterpart. Besides, an intermediary “upward frequency” approximation is introduced as a beneficial tradeoff between the accuracy of nonperturbative noise computations and the reliability of linear theory noise computations. Overall, the proposed strategies show great potential for the simulation of the noise resulting from mechanical vibrations.