The analyses of the influence of spatial harmonics on the electromagnetic torque of the multi-phase induction machine and reducing this influence are important tasks to ensure the high efficiency of the induction machine. Designing the machine to consider the influence of spatial harmonics is essential to ensure the desired mechanical and energy characteristics. In the case of the sinusoidal winding supply of the induction machine, the magnetomotive force has high spatial harmonics, which are caused by the machine-winding design. The interaction between the 5th, 7th, 11th and 13th spatial harmonics of the winding function and the first time-harmonic of the winding supply causes the appearance of the 6th and 12th harmonics in the electromagnetic torque of the machine. A prototype of the symmetrical six-phase induction machine and the experimental study for the influence of spatial harmonics on the harmonic content of the stator currents in different machine modes are given in this paper. The mathematical model of the six-phase induction machine has been developed using the average voltages in integration step method. The introduction of the harmonic components into the magnetization inductance in the mathematical model of the six-phase induction machine for taking into account the spatial harmonics of the machine-winding function is proposed in this paper. The adequacy of the mathematical model was confirmed by comparing the simulation and experimental results. The harmonic content of the electromagnetic torque, which is caused by spatial harmonic influence, is analyzed.