Motor mounting system is designed so that the torsional mode resonant or natural frequency is less than twice the frequency of the motor power supply divided by the square root of two (√2). The illustrated mounting arrangements are "soft" with respect to torsional mode vibrations, and yet are "stiff" with respect to axial and tilting mode vibrations. In one arrangement, lugs are formed preferably from a tough and strong sheet or strip material that is thicker and substantially stronger and stiffer (even in the radial vibration mode) than would usually be desirable from a torsional vibration isolation standpoint, but means are provided for promoting flexure in the vicinity of the parts of the lugs that will be subject to the most flexure or deflection. These flexure promoting means may be in the form of tuning apertures formed along a preselected, longitudinally extending neutral axis of each lug so that the strength of the lug will not be objectionably compromised for axial loading conditionss. It is preferred to select the tuning means so that the cumulative effective spring constant (in pound-inches per radian) of the mounting lugs will be less than the quantity (2.84× Ip×10 5 ), where Ip is the polar moment of inertia measured in pound-inches-seconds 2 . Also illustrated are mounting band members and torsionally flexible arms that interfit one with another in a slotted interrelationship. Ends of the arms are folded under a band member so that the ends of the arms are securely trapped by the band member against the outer peripheral surface of the motor. This technique assures that the motor will remain supported by the band member and arms, and minimizes the degree of weld or other fastener strength that would otherwise have to be provided between the arms and motor.