A theory is presented of mutual steric exclusion of protein molecules and randomly coiled polymer molecules, in which the former are presented as impenetrable rigid particles and the latter as flexible segmented chains obeying Gaussian statistics. The limiting case of small polymer chains and large protein molecules is treated first, by approximating the protein surface as planar; this gives an excluded volume equal to the sum of protein volume V and a term in Vh0/R, i.e., protein volume times the ratio of rms end-to-end distance of the polymer and radius of the protein. Several cases of steric exclusion are treated next, using a quite general approach, by which excluded volume can be expressed as V/〈m〉, the ratio of protein volume and the average number of elements that are simultaneously excluded by, or that simultaneously exclude, one protein molecule. Expressions for 〈m〉 are successively obtained for thin rods arbitrarily finely divided into segments, for uniformly randomly distributed segments, for segments linked into very long polymers, and for segments linked into finite polymers. In all these cases the protein is represented as a sphere; in addition an expression for the excluded volume of very long polymers and cylindrical protein molecules is obtained. Excluded volume of spherical proteins and very long polymers is found to be simply proportional to the radius of the protein and the square of the rms end-to-end distance of the polymer, while the larger excluded volume of proteins and finite chains is conveniently expressed as the product of the result for very long chains and a series expansion in powers of R/h0. Comparison with results of Monte Carlo simulation shows all predictions of theory to be excellent, with two exceptions. As a result of the use of Gaussian statistics for polymers of any chain length, the theory does not adequately describe the case of stiff polymer chains and small protein molecules. As a result of a second, at present unavoidable, approximation in the calculation of 〈m〉 for polymers of finite chain length, theory systematically predicts excluded volumes that are too low by a factor that varies from 1 to 2. As a result, this theory makes useful predictions for short polymers, as long as h0/R does not exceed 1 and for long polymers, as long as R/h0 does not exceed 0.5. Comparison with experimental data is found to be good; the prediction of proportionality of excluded volumes of globular proteins and high molecular weight polymers with protein radius agrees with recent observations with poly(ethylene oxide) and predicted excluded volumes of serum albumin and this polymer at three different polymer molecular weights agree within 10% with recently observed values.