A comparative study of numerical modelling and laboratory experiments of two-phase immiscible displacements in a 33 cm x 10 cm x 3 cm thick cross-bedded reservoir model is reported. Dynamic two-dimensional fluid saturation development was obtained from experiments by use of a nuclear tracer imaging technique and compared to numerical predictions using a full-field black oil simulator. The laboratory cross-bedded reservoir model was a sandpack consisting of two strongly water-wet sands of different grain sizes, packed in sequential layers. The inlet and outlet sand consisted of low permeable, high capillary, sand while the central crosslayer with a dip angle of 30 degrees, was a high permeable, low capillary, sand. Results on moderate contrasts in permeability and capillary heterogeneities in the cross-bedded reservoir model at different mobility ratios and capillary number floods temporarily showed a bypass of oil, resulting in a prolonged two-phase production. The final remaining oil saturations, however, were as for isolated samples. Hence, permanently trapped oil was not observed. Simulations of waterfloods, using a commercial software package, displayed correct water breakthrough at low flow rate and unity viscosity ratio, but failed in predicting local saturation development in detail, probably due to numerical diffusion. The simulator was used to test several cases of heterogeneity contrasts, and influence from different relative permeability curves. Further, by altering the capillary pressure at the outlet, the end effects were proven important.