Pressure losses as friction factor, and flow patterns in 3D axial flow between sinusoidal corrugated parallel plates with perpendicular directions of corrugation is numerically studied. The flow is assumed to be steady and laminar in the studied range. The numerical procedure is Chorin's artificial compressibility method with finite difference second order central discretization. Results show that in moderate Reynolds numbers, vortices are formed and they put a great effect on pressure drop. The size of vortices grows with increase in Reynolds number, and also their cores tend to shift toward the flow direction and away from the walls. These vortices are not closed loops, and the streamlines slightly swirl in the circulating zone of vortices. This means that there can be a little convection in these regions and they are not closed dead zones anymore. The linear curve fit of the friction factor diagrams versus Reynolds number in logarithmic scale, shows that friction factor almost obeys a power function of hydraulic Reynolds number in the investigated geometries. With a slight error, this can be assumed as a rough estimation for the product of friction factor and hydraulic Reynolds number. The friction factor grows larger with increase in wave amplitude or decrease in wavelength. Also, when the gap between two plates decreases, friction factor increases. The least friction factor among the investigated geometries is for flat parallel plates. (C) 2010 Elsevier Ltd. All rights reserved.