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A statistical mechanical approach to the protein folding problem is developed based on computer simulations. The properties of proteins related to conformation and folding are determined from the density of states of the protein. A new simulation procedure, the Entropy Sampling Monte Carlo method, is used to determine accurately the density of states of the protein. To enhance the efficiency of sampling the conformational space of a protein, two techniques (a conformational-biased chain regrowth procedure and a jump-walking method) were introduced into the simulation. Applications of the approach to study a number of model polypeptides and a small protein, Bovine Pancreatic Trypsin Inhibitor, have been carried out. The results obtained demonstrate that the new approach is more powerful and produces richer information about the thermodynamics and folding behavior of proteins than conventional simulation methods.