An algorithm for the rapid analytical determination of the accessible surface areas of solute molecules is described. The accessible surface areas as well as the derivatives with respect to the Cartesian coordinates of the atoms are computed by a program called “MSEED,” which is based in part on Connolly's analytical formulas for determining surface area. Comparisons of the CPU time required for MSEED, Connolly's numerical algorithm DOT, and a program for surface area determination (ANA) based on Connolly's analytical algorithm, are presented. MSEED is shown to be as much as 70 times faster than ANA and up to 11 times faster than DOT for several proteins. The greater speed of MSEED is achieved partially because nonproductive computation of the surface areas of internal atoms is avoided. A sample minimization of an energy function, which included a term for hydration, was carried out on MET‐enkephalin using MSEED to compute the solvent‐accessible surface area and its derivatives. The potential employed was ECEPP/2 plus an empirical potential for solvation based on the solvent‐accessible surface area of the peptide. The CPU time required for 150 steps of minimization with the potential that included solvation was approximately twice as great as the CPU time required for 150 steps of minimization with the ECEPP/2 potential only.