A new algorithm is presented to calculate the analytical molecular surface defined as a smooth envelope traced out by the surface of a probe sphere rolled over the molecule, The core of the algorithm is the sequential build up of multi-are contours on the van der Waals spheres. This algorithm yields substantial reduction in both memory and time requirements of surface calculations. Further, the contour-buildup principle is intrinsically ''local'', which makes calculations of the partial molecular surfaces even more efficient, Additionally, the algorithm is equally applicable not only to convex patches, but also to concave triangular patches which may have complex multiple intersections. The algorithm permits the rigorous calculation of the full analytical molecular surface for a 100-residue protein in about 2 seconds on an SGI indigo with R4400 processor at 150 Mhz, with the performance scaling almost linearly with the protein size. The contour-buildup algorithm is faster than the original Connolly algorithm an order of magnitude. (C) 1996 Academic Press, Inc.