The free vibration analysis of torsional line shafts is the preliminary step for any torsional forced vibration system and, in certain cases, can be sufficiently accurate. This work introduces a stream-lined approach for free vibration analysis of the torsional line of a four-stroke engine with four cylinders (operating range 600–5500 rpm). The equivalent torsional model, calculated by the British International Combustion Engine Research Association empirical method, has eighteen degrees of freedom. On the basis of some simplifying hypothesis, the equations of motion are obtained using Lagrange’s formalism. Then the Rutishuser method is used to calculate natural frequencies and mode shapes. The main objective is to determine particularly dangerous crankshaft rotational speeds, as well as the magnitudes of the torsional vibrations of the different disks during resonance. The adaptation example of the motor shaft line shows that for the investigated configuration a speed of 710 rpm (importance 2.36 for harmonic 2), is a particularly dangerous rotational speed for the entire operating range of the motor.