The most common practice when designing high speed synchronous reluctance (SyR) machine consists in performing the electromagnetic design followed by a finite element rotor structural verification at the maximum operating speed. This approach could lead to sub-optimal designs because it neglects the effect of the rotor structural parts on the electromagnetic performance and vice versa. In order to properly address the interaction of the magnetic and structural design aspects for the design of high speed SyR machines, two multi-physics design approaches, both based on multi-objective stochastic optimization algorithms and finite element analysis are presented. The first procedure performs a physically decoupled design, in which the electromagnetic optimization is followed by a proper mechanical optimization. The second approach executes a truly physically coupled design. The two approaches are compared in terms of performances of the final designs and required computational time. The results presented here are intended to be used as general guidelines for the design of high speed SyR machines.