In this manuscript, we develop a two-dimensional coarse-grained model to study equilibrium properties of fibril-like structures made of amyloid proteins. The phase space of the model is sampled using Monte Carlo computer simulations. At low densities and high temperatures proteins are mostly present as monomers while at low temperatures and high densities particles self-assemble into fibril-like structures. The phase space of the model is explored and divided into different regions based on the structures present. We also estimate free-energies to dissociate proteins from fibrils based on the residual concentration of dissolved proteins. Consistent with experiments, the concentration of proteins in solution does not affects their equilibrium state. Also, we study the temperature dependence of the equilibrium state to estimate thermodynamic quantities, e.g., heat capacity and entropy, of amyloid fibrils. (C) 2019 Elsevier B.V. All rights reserved.