In shallow water, and specifically for minimum structures, the critical wave height exponent α has been shown to vary significantly with structural configuration. Because of the strong relationship to the wave kinematics, α is also sensitive to the wave theory chosen. The North West Shelf offshore Australia has numerous minimum structures located in relatively shallow water, which requires non-linear wave theory. In the near-breaking condition, estimation of the wave crest kinematics is difficult, with Stream Function theory being the most widely used. However, various other wave theories and nonlinear numerical techniques have been developed to predict wave kinematics for shallow water conditions. The following wave theories are compared: regular Stream Function theory, Cnoidal wave theory, Stokes’ theory, NewWave theory, and a second-order correction to NewWave theory. Kinematics, loads and α results are presented for a cylinder in three different water depths.