Abstract: A compliant engagement member for use with tree-shaking apparatus that resists deformation along the axis of vibration, thereby avoiding dissipation of vibrational energy, yet allows sufficient off-axis deformation to prevent slippage and consequent abrasion of the tree. The engagement member of the present invention preferably includes a rigid shaker pad; a sling that retains the shaker pad against the arm of a shaking device; a sealed, lubricant-filled pouch, extending from the sling; and a contact blanket, which is draped over the pouch and makes contact with the tree. In operation, lateral inward movement of the shaking device compresses the lubricant pouch against the interior of the contact blanket. The pouch is packed sufficiently tightly with lubricant to resist deformation as a result of this compression. However, the pouch accommodates deformation in the direction transverse to the axis of vibration, thereby absorbing transverse movement and preventing its transmission to the tree.