Non-synonymous single-nucleotide polymorphism (nsSNP) of genes introduces amino acid changes to proteins, and plays an important role in providing genetic functional diversity. To understand the structural characteristics of disease-associated SNPs, we have mapped a set of nsSNPs derived from the online mendelian inheritance in man (OMIM) database to the structural surfaces of encoded proteins. These nsSNPs are disease-associated or have distinctive phenotypes. As a control dataset, we mapped a set of nsSNPs derived from SNP database dbSNP to the structural surfaces of those encoded proteins. Using the alpha shape method from computational geometry, we examine the geometric locations of the structural sites of these nsSNPs. We classify each nsSNP site into one of three categories of geometric locations: those in a pocket or a void (type P); those on a convex region or a shallow depressed region (type S); and those that are buried completely in the interior (type I). We find that the majority (88%) of disease-associated nsSNPs are located in voids or pockets, and they are infrequently observed in the interior of proteins (3.2% in the data set). We find that nsSNPs mapped from dbSNP are less likely to be located in pockets or voids (68%). We further introduce a novel application of hidden Markov models (HMM) for analyzing sequence homology of SNPs on various geometric sites. For SNPs on surface pocket or void, we find that there is no strong tendency for them to occur on conserved residues. For SNPs buried in the interior, we find that disease-associated mutations are more likely to be conserved. The approach of classifying nsSNPs with alpha shape and HMM developed in this study can be integrated with additional methods to improve the accuracy of predictions of whether a given nsSNP is likely to be disease-associated.