Abstract <p>The problem of microscopic Stokes flow in a porous medium of a mixed fibrous filter composed of multiple randomly distributed micro- and nanofibers with circular cross-sections has been solved. The boundary value problem for the stream function satisfying the biharmonic equation is solved using the boundary element method with truncated Fourier series expansions of the unknown functions. Parametric studies of the flow field and drag forces were performed for the mixed filter containing up to ten thousand fibers. The advantages of the method used are demonstrated.</p>