Quasi-one-dimensional (quasi-1D) tools developed for capturing flow and acoustic dynamics in non-segmented solid rocket motors are evaluated using multi-dimensional computational fluid dynamic simulations and used to characterise damping of modal perturbations. For motors with high length-to-diameter ratios (of the order of 10), remarkably accurate estimates of frequencies and damping rates of lower modes can be obtained using the the quasi-1D approximation. Various grain configurations are considered to study the effect of internal geometry on damping rates. Analysis shows that lower cross-sectional area at the nozzle entry plane is found to increase damping rates of all the modes. The flow-turning loss for a mode increases if the more mass addition due to combustion is added at pressure nodes. For the fundamental mode, this loss is, therefore, maximum if burning area is maximum at the centre. The insights from this study in addition to recommendations made by Blomshield(1) based on combustion considerations would be very helpful in realizing rocket motors free from combustion instability.