Air-core pulsed alternator has been a promising pulsed power supply for electromagnetic launching system, due to its characteristics of high power density and high energy density, especially on the occasion with restriction of weight and volume. It is made of non-ferromagnetic materials and especially the rotor is constructed by titanium alloy with high specific strength. That means the air-core pulsed alternator can run at a much higher tip speed compared with that of conventional iron-core machines, which has a great improvement in the energy storage density. But high speed leads to big challenges such as huge centrifugal forces on rotor and vibration phenomenon, and both of them should be taken into consideration carefully.In this text, a typical rotor structure of air-core pulsed alternators is introduced in detail. Then, the stress calculation and simulation about rotor components are carried out when the machine operates in normal. Also, in order to avoid the harsh situation of resonance, the influence of bearing's radius and its mounting position on the critical speed is analyzed. The actual vibration mode and critical speed of the rotor are given at the selected radius and position. The above research has important significance to optimize and fabricate the prototype.