Promising attributes in data processing such as faster read/write times, longer retention, and superior scalability have put resistive switching memristors in the spotlight of research. This thesis presents a numerical method to determine the variability in switching that different memristors exhibit. Current-voltage relationships and cyclic voltage sweeps are gathered from specific memristor devices with various geometrical configurations. Using the inverse sampling method and Monte Carlo simulations, the variation in switching characteristics for these memristors are characterized by a phenomenological approach. Further, randomness is introduced to assess the effect of geometric parameters in a probabilistic model and trends within the response. The model is validated by comparison with experimental data reported in the literature. The presented model is effective in capturing the variation in memristor responses. This, has been shown to be an important attribute in neuromorphic computing applications, and can aid experimentalists and manufacturers in refining memristor designs.