We study the thermodynamic properties of the experimental fragments of the amyloid fibril made of the HET-s prion proteins (the infectious element of the filamentous fungus Podospora anserina) and of amyloid-beta proteins (the major component of Alzheimer's disease-associated plaques) by using the three-dimensional molecular theory of solvation. The full quantitative picture of hydration effects, including the hydration thermodynamics and hydration structure around the fragments, is presented. For both the complexes, the hydration entropic effects dominate, which results in the entropic part offsetting the unfavorable energetic part of the free energy change upon the association. This is in accord with the fact that the hydrophobic cooperativity plays an essential role in the formation of amyloid fibrils. By calculating the partial molar volume of the proteins, we found that the volume change upon the association in both the systems is large and positive, with the implication that high pressure causes destabilization of the fibril. This observation is in good agreement with the recent experimental results. We also found that both the HET-s and amyloid-beta pentamers have loose intermolecular packing with voids. The three-dimensional molecular theory of solvation predicts that water molecules can be locked in the interior cavities along the fibril axis for both the HET-s and amyloid-beta proteins. We provide a detailed molecular picture of the structural water localized in the interior of the fibrils. Our results suggest that the interior hydration plays an important role in the structural stability of fibrils.