In cooling towers packed with trickle or splash fills, which have anisotropic flow resistance, the air flow through the fill is oblique or in cross-counterflow to the water flow, particularly at the cooling tower inlet when the fill loss coefficient is small or when the fill hangs down into the air inlet region. This results in that the fill Merkel number or transfer characteristic for cross-counter flow is between that of purely counter- and crossflow fills. When using CFD to model natural draught wet-cooling tower performance for isotropic fill resistance, two- or three-dimensional models are therefore required to determine fill performance. In this paper, the governing fundamental partial differential equations are derived in cylindrical and Cartesian coordinates to determine the cooling water temperature, water evaporation rate, air temperature, and air humidity ratio in two-dimensional cross-counterflow fills for both saturated and supersaturated air. To solve these equations, a relation is proposed to determine Merkel numbers for oblique air flows by linear interpolation and extrapolation of purely cross- and counterflow Merkel numbers in terms of the air flow angle. This model is compared to analytical Merkel numbers obtained for different air flow angles using a single drop trajectory model. A linear upwind computational model and an Eulerian FLUENT ® model are developed to evaluate fill performance characteristics from test data and to model fill performance in cooling towers, respectively. The results of these two models are compared and verified with a FLUENT Euler–Lagrange model, showing minor deviations.