Abstract: A downhole probe for use in conditions of high vibration or shock comprises a vibration-sensitive inner unit having a cylindrical outer surface, an outer casing having a cylindrical inner surface within which the inner unit is accommodated, and an intermediate vibration-damping composite sleeve extending between said inner and outer surfaces. The composite sleeve has two coaxial sleeve parts fitting one within the other and consisting of an apertured metal sleeve part and an elastomeric sleeve part having axial ribs which extend through axial slots in the apertured sleeve part. The axial ribs of the elastomeric sleeve part engage the inner surface of the outer casing and inner surfaces of the elastomeric sleeve part engage the outer surface of the inner unit so as to support the inner unit within the outer casing in such a manner as to provide efficient isolation of the inner unit from external vibration and shock.