The Costas loop circuit was invented in the 1950s. It is widely used for carrier recovery and demodulation. A rigorous nonlinear analysis of the Costas loop circuit is a complicated task, so engineers frequently use simplified mathematical models and numerical simulation. It is shown that the analysis of a simplified model of the classical Costas loop without justification can lead to wrong conclusions on the dynamics of the circuit. A nonlinear model of the classical Costas loop is derived and rigorously justified on the basis of the averaging method.