- Summary The complexity of subsurface flow systems calls for a variety of concepts leading to the multiplicity of simplified flow models. One habitual simplification is based on the assumption that lateral flow and transport in unsaturated zone are not significant unless the capillary fringe is involved. In such cases the flow and transport in the unsaturated zone above groundwater level can be simulated as a 1D phenomenon, whereas the flow and transport through groundwater are viewed as 2D or 3D phenomena. A new approach for a numerical scheme for 3D variably saturated flow using quasi 3D Richards’ equation and finite difference scheme is presented. The corresponding numerical algorithm and the QUASI-3D computer code were developed. Results of the groundwater level simulations were compared with transient laboratory experimental data for 2D data constant–flux infiltration, quasi-3D HYDRUS-MODFLOW numerical model and a FULL-3D numerical model using Richards’ equation. Hypothetical 3D examples of infiltration, pumping and groundwater mound dissipation for different spatial–time scales are presented. Water flow simulation for the Alto Piura aquifer (Peru) demonstrates the QUASI-3D model application at the regional scale. Computationally the QUASI-3D code was found to be more efficient by an order of 10–300%, while being accurate with respect to the benchmark fully 3D variable saturation code, when the capillary fringe was considered.