We suggest a theoretical method based on thestatistical mechanics for treating the Α-helix↔random coil transition in polypeptides. This process is considered as a first-order-like phase transition. The developed theory is free of model parameters and is based solely on fundamental physical principles. We apply the developed formalism for the description of thermodynamical properties of alanine polypeptides of different length. We analyze the essential thermodynamical properties of the system such as heat capacity, phase transition temperature and latent heat of the phase transition. Alternatively, we have obtained same thermodynamical characteristics from the molecular dynamics simulations and compared the results with the results of statistical mechanics calculation. The comparison proves the validity of the statistical mechanics approach and establishes its accuracy.