A calculation procedure for two-dimensional elliptic flow is applied to predict the pressure drop and heat transfer characteristics of laminar and turbulent flow of air across tube banks. The turbulence model used involves the solution of two partial differential equations, one for the kinetic energy of the turbulence and the other for its dissipation rate. These differential equations are solved simultaneously with those for the conservation equations of mass, momentum and energy using an implicit finite volume procedure. The numerical methodology utilizes the stepped boundary technique to approximate the tube surface which is kept at constant temperature. The computations are extended to cover the case of two rows of tubes undergoing cross flow with in-line and staggered tube arrangements besides the case of a single row. Thereby, Reynolds number (Re) as well as the normal and parallel tube spacing-to-diameter ratios are varied. Effects of the flow and the geometry parameters on the friction factor and the local and global Nusselt number are presented. Moreover, velocity vector diagrams and temperature contours as well as axial flow velocity and turbulence kinetic energy profiles along the flow field upstream, over and downstream the tubes are also given. The theoretical results of the present model are compared with previously published experimental data of different authors. Satisfactory agreement is demonstrated.