A model is proposed for predicting the intrinsic rejections of linear flexible molecules, of high molecular dimensions, in microfiltration and ultrafiltration membranes. The developed model is based on the available theory of hindered transport of solutes through narrow pores, assuming that convection is the only relevant transport mechanism. For the application of the model, partition coefficients of the solutes between the solution and the membrane were estimated by a stochastic simulation, assuming suction of the macrosolutes into the pore. In these simulations, the macromolecules were modeled as freely jointed chains. Different methods for the estimation of the molecular dimensions of the solutes are discussed. The validity of the model was tested using dextran T2000 and plasmid pUC19 in its linear isoform, as model solutes; the tests were performed using membranes of different pore size, that include two ultrafiltration membranes previously characterized, having 4.1 and 10.5 nm of pore radius, and two track-etched polycarbonate membranes, having 15 and 40 nm of pore radius. Filtration was performed in a stirred cell, at controlled permeate flux. Different conditions of stirring speed and permeate flux were tested to check the consistency of the model. The results show that very satisfactory predictions are obtained, considering the simplicity of the model, especially in the case of the plasmid.