The solubility parameters, delta, of several asphaltene models were, calculated by mean of an atomistic NPT ensemble. Continental and archipelago models were explored. A relationship between the solubility parameter and the molecule structure was determined. In general, increase of the fused-rings number forming the aromatic core and the numbers of heteroatoms such as oxygen, nitrogen, and sulfur produces an increase of the solubility parameter, while increases of the numbers and length of the aliphatic chains yield a systematic decrease of this parameter. Molecules with large total carbon atom number at the tails, no and small aromatic ring number, n(r), exhibit the biggest values of delta, while molecules with small n(c) and large n(r) show the smallest delta values. A good polynomial correlation delta = 5.967(n(r)/n(c)) - 3.062(n(r)/n(c))(2) + 0.507 (n(r)/n(c))(3) + 16.593 with R-2 = 0.965 was found. The solubilities of the asphaltene models in toluene, heptane, and amphiphiles were studied using the Scatchard-Hildebrand and the Hansen sphere methodologies. Generally, there is a large affinity between the archipelago model and amphiphiles containing large aliphatic tails and no aromatic rings, while continental models show high affinity for amphiphiles containing an aromatic ring and small aliphatic chains.