Fatigue damage assessment under random vibration is essential for ensuring structural durability. Traditional spectral methods, while efficient for Gaussian loads, fail to capture the effects of non-Gaussian excitation. This limitation is often addressed using a correction coefficient applied to the frequency-domain fatigue damage, accounting for the kurtosis and skewness of the stress response. The latters can be derivable via a modal approach but a transient analysis is still required. To overcome this, the present work introduces the Modal Central Moments Spectra (MCMS), a novel method enabling efficient computation of higher-order moments. By caching modal central moments and mixed terms, MCMS eliminates the need for time-domain simulations and element-wise stress evaluations. Once derived for a given excitation, these spectra can be reused across different structural configurations, drastically reducing computational cost. Validation demonstrates the accuracy and efficiency of MCMS, making it a valuable tool for vibration fatigue assessment under non-Gaussian random loads.