Computational protein sequence design is the rational design based on computer simulation of new protein molecules to fold to target three-dimensional structures, with the ultimate goal of designing novel functions. It requires a good understanding of the thermodynamic equilibrium properties of the protein of interest. Here, we consider the contribution of the solvent to the stability of the protein. We describe implicit solvent models, focusing on approximations of their nonpolar components using geometric potentials. We consider the surface area (SA) model in which the nonpolar solvation free energy is expressed as a sum of the contributions of all atoms, assumed to be proportional to their accessible surface areas (ASAs). We briefly review existing numerical and analytical approaches that compute the ASA. We describe in more detail the alpha shape theory as it provides a unifying mathematical framework that enables the analytical calculations of the surface area of a macromolecule represented as a union of balls.