In this work, the changes in eigenfrequencies of flexible appendages with • :various mass ratios of space vehicles due to the allowance of a rigid body. motion are studied. These changes are governed by the difference eigen-value problem [2] which is formulated in terms of the generated effective :mass and stiffness matrices. The computation techniques for calculating .• the upper and lower bounds of the dominant eigenfrequencies are performed :by the utilization of the bound formula approach [1] . An example of the transverse vibration analysis of the fuslage-wing combination with diff-erent mass ratios in different zones of vibratory motion is solved . A :'comparison between the computed calculations and previously published re-sults [0] is presented