Hydrodynamic response characteristics of classic and other Spar geometries have been investigated in the past using experimental and numerical studies in regular waves. The response of such floating system in regular waves has been reasonably established. However, in real sea condition, the existence of multiple wave frequencies in a sea state may alter the response, when the excitation frequency has the component of resonant frequency of the hull. The wave energy at the resonant frequency of the design wave spectrum is generally small, but may lead to large motion like Mathieu-type instability caused by the heave–pitch coupling effects, when the pitch/heave natural frequency ratios are critical (0.5, 1.0, 2.0, etc.). Various alternatives to reduce the heave motion of the Spar platform such as decreasing the water plane area, increasing the draft, added mass and/or damping have been in the fore front of recent research. Buoy form Spar proposed in this paper has a reduced diameter near the water plane. The motion response of such Spar in regular waves has been presented in another paper published in this journal; the heave response under random waves is presented in this paper. A classic Spar, with constant hull cross section diameter of 31 m and buoy form Spars with reduced water plane diameter of 25 and 20 m with draft of 12.5 m and displacement of 63,200 tons were considered for the study. The experimental and numerical investigations were conducted on 1:100 scale models. The pitch/heave natural frequency ratios of CLS-31, BFS-25 and BFS-20 Spars are 0.5, 0.667 and 1.0, respectively. CLS-31 and BFS-20 are vulnerable to Mathieu-type instability, since their pitch/heave natural frequency ratios are 0.5 and 1.0. Based on the study, it is concluded that the reduction in water plane area reduces the response in random waves and reduces the susceptibility to Mathieu instability. © 2016 Informa UK Limited, trading as Taylor & Francis Group.