This paper presents a theoretical analysis of the kinetics of osmotic transport across a semipermeable membrane. There is a thermodynamic connection between the rate of flow under a hydrostatic pressure difference and the rate of flow due to a difference in solute concentration on the two sides. One might therefore attempt to calculate the osmotic transport coefficient by applying Poiseuille's equation to the flow produced by a difference in hydrostatic pressure. Such a procedure is, however, inappropriate if the pores in the membrane are too small to allow molecules to “overtake.” It then becomes necessary to perform a statistical calculation of the transport coefficient, and such a calculation is described in this paper. The resulting expression for the number of solvent molecules passing through a pore per second is J = m D1 δn1/l2 where m is the number of solvent molecules in the pore, l is the length of the pore, D1 is the self-diffusion coefficient of the solute, and δn1 the difference in solvent mole fraction on the two sides of the membrane. This equation is used for estimating the number of pores per unit area of the squid axon membrane; the result is 6 × 109 pores/cm2.