A two-dimensional numerical model, based on the elliptic Navier-Stokes equations, is developed to predict the location of incipient instability, xfr, in low Reynolds number water flows in vertical annuli. Results show that neglecting the radial momentum can underpredict the values of xfr at high Grq/Re values by as much as 45%. Conversely, the axial momentum diffusion only insignificantly affects the velocity fields and, hence, the accuracy of predicting xfr. The results of a parametric analysis investigating the effects of various operating conditions and geometrical parameters is used to develop general criteria for predicting the onset of flow instability in vertical annuli. These criteria are within ± 10 and ± 15% of the experimental data for buoyancy assisted and opposed flows, respectively.