This paper presents an analytical method to compute the magnetic flux distribution in spoke interior permanent-magnet (IPM) machines with non-magnetic shaft from no-load to short-circuit conditions. Despite non-magnetic shaft gets significant reduction of the PM leakage flux, this cannot be neglected to calculate correct flux distribution; thus, shaft leakage flux is analyzed and modelled. Moreover, as the demagnetization characteristic of the machine depends on the magnetic circuit, simple mathematical equations to estimate the demagnetization level of the magnets are also given. Based on this approach, protection against demagnetization due to short-circuit current and maximum field-weakening level achievable are easily estimated. The presented formulation and methods are used to optimize the rotor of an IPM machine in order to maximize the electromagnetic torque (30% higher), minimize the amount of PM material, and protect PMS against demagnetization under field-weakening and short-circuit conditions. Analytical results are compared with finite-element software, showing errors lower than 4% in the no-load magnetic circuit and lower than 12% at short-circuit conditions. Presented formulation and methods have very low computation time, so the design process time of spoke IPM machines is significantly reduced. The proposed analytical approach is also applicable to other PM machines.