The accurate prediction of wave runup on deepwater offshore platform columns is of great importance for design engineers. Although linear predictive models are commonly used in the design and analysis process, many of the important effects are of higher order, and thus can only be accounted for by complex nonlinear models that better reflect the physics of the problem. This study presents a two-parameter Weibull distribution function that utilizes empirical coefficients to model the surface wave runup. Laboratory measurements of irregular waves interacting with vertical platform cylinders were used to obtain the Weibull coefficients necessary for the analytical model. Six data sets with different configurations where the wave elevation was measured close to the test cylinders are analyzed. These data on wave runup in deepwater random waves were generated at similar water depths with identical significant wave heights and spectral peak periods. Statistical parameters, zero crossing analysis and spectral analysis were utilized to characterize and interpret the time series data. The analysis focused on interpreting the tails of the probability distributions by carefully fitting the analytical model to the measured model data. This study demonstrates that the two-parameter Weibull model can be used to accurately model the wave runup on platform cylinders for the range of experimental data investigated in this study.