A new method for exact analytical calculation of the accessible surface areas and their gradients with respect to atomic coordinates is described. The new surface routine, GETAREA, finds solvent-exposed vertices of intersecting atoms, and thereby avoids calculating buried vertices which are not needed to determine the accessible surface area by the Gauss–Bonnet theorem. The surface routine was implemented in FANTOM, a program for energy minimization and Monte Carlo simulation, and tested for accuracy and efficiency in extensive energy minimizations of Met-enkephalin, the α-amylase inhibitor tendamistat, and avian pancreatic polypeptide (APP). The CPU time for the exact calculation of the accessible surface areas and their gradients has been reduced by factors of 2.2 (Met-enkephalin) and 3.2 (tendamistat) compared with our previous approach. The efficiency of our exact method is similar to the recently described approximate methods MSEED and SASAD. The performance of several atomic solvation parameter sets was tested in searches for low energy conformations of APP among conformations near the native X-ray crystal structure and highly distorted structures. The protein solvation parameters from Ooi et al.[Proc. Natl. Acad. Sci. USA, 84, 3086 (1987)] and from Wesson and Eisenberg [Prot. Sci., 1, 227 (1992)] showed a good correlation between solvation energies of the conformations and their root-mean-square deviations from the X-ray crystal structure of APP.© 1998 John Wiley & Sons, Inc. J Comput Chem 19: 319–333, 1998