Upper limits on the masses of stars that can form are reexamined and models for the inflow of matter through cocoons around stars of 60, 100, and 200 solar masses are calculated. Consideration is given to the general conditions that must hold at the inner and outer boundaries of a protostellar cocoon; limits on the dust-to-gas ratios and mass inflow rates that will permit inflow onto very massive stars are determined. It is found that inflow can occur if intermediate-sized grains (0.05-0.25 micron) are missing from the initial gas/dust mixture. The existence of massive stars in certain locations in galaxies indicates that preconditioning of the interstellar medium by shocks or turbulence is necessary for massive star formation.