The paper presents a novel simulation tool which can be used for numerical analysis of nonlinear circuits and systems forced by strong noise sources and perturbed by weak periodic signals. The methodology, which is based on linear-response theory, is universal in scope and can be applied to all topologies without restraints on the dimensionality of the structure or the size of the parameter set. The main purpose of the developed algorithm is to enable efficient numerical analysis of nonlinear noise-driven circuits and systems with emphasis on stochastic resonance. Currently, computationally expensive Monte-Carlo methods often constitute the only other option available for simulation in these cases. Linear-response models have previously been developed for the 1-dimensional canonical scenario but it will be shown that these specialized formulations can not be directly adapted to higher dimensional systems. Compared to a simple Monte-Carlo integration scheme, the computational efficiency following from the proposed algorithm is improved by several orders of magnitude.