In the present investigation, statistical and chaos analysis techniques were implemented to evaluate pressure dynamics in air-water, vertical pipe flow. The purpose of the analysis is to relate the statistical and chaos measures to the flow physics. Pressure measurements were achieved in a 22 mm ID aluminum and quartz tubing test section. Four water superficial velocities (0.0055, 0.055, 0.165 and 0.329 m/s) were examined for a range of air superficial velocities. Detailed statistical and chaos results are presented for signals representing slug flow, churn flow, and annular flow. Statistical analyses included qualitative evaluation of the shape of histograms, calculation of normalized statistical moments, and implementation of a nonlinearity test. Kolmogorov entropy and attractor dimension estimates (maximum-likelihood correlation dimension and correlation dimension) comprised the chaos analysis measures. The non-integer values of maximum-likelihood correlation dimension and correlation dimension are consistent with chaotic systems. Additionally, the positive, non-infinite values of Kolmogorov entropy, ranging from 5 to 107 bits/s, provide further evidence of the chaotic nature of the air-water vertical upflow.