External transverse laminar flow of a viscous incompressible fluid and convective diffusion of a solute in a model membrane contactor with a regular system of monodisperse fibers have been numerically simulated. A row of equally spaced parallel fibers was taken as the simplest model system, for which the dependences of the drag force and the efficiency of solute absorption by the fiber (Sherwood number of fiber) upon the distance between the axes of adjacent fibers, and the Reynolds and Peclet numbers have been calculated. The influence of the flow inertia has been studied, and it has been shown that the flow field and mass transport in the contactor can be described in terms of the linear Stokes approximation up to as high Reynolds numbers as dense is the fiber array.