The effects of crowding on the self or tracer diffusion of macromolecules in concentrated solutions is an important but difficult problem, for which, so far, there has been no rigorous treatment. Muramatsu and Minton suggested a simple model to calculate the diffusion coefficient of a hard sphere among other hard spheres. In this treatment, scaled particle theory is used to evaluate the probability that the target volume for a step in a random walk is free of any macromolecules. We have improved this approach by using a more appropriate target volume which also allows the calculation to be extended to the diffusion of a hard sphere among hard spherocylinders. We conclude that, to the extent that proteins can be approximated as hard particles, the hindrance of globular proteins by other proteins is reduced when the background proteins aggregate (the more so the greater the decrease in particle surface area), the hindrance due to rod-shaped background particles is reduced slightly if the rod-like particles are aligned, and the anisotropy of the diffusion of soluble proteins among cytoskeletal proteins will normally be small.