The clathrate compound Eu8Ga16Ge30 with the type-I cubic structure is expected to show rattling motion of Eu atom which is an anomalous off-center oscillation. To investigate an influence of rattling motion to the lattice system of Eu8Ga16Ge30, we have measured temperature T dependence of elastic modulus (C11-C12)/2 and ultrasonic attenuation α of a single-crystalline sample in the T range between 4.2 and 150K for ultrasonic frequencies from 20 to 150MHz. We found ultrasonic frequency dependence in both (C11-C12)/2 and α, suggesting rattling motion of Eu atoms between 50 and 100K. We obtained a relaxation time 6.0×10-11s and an excitation energy 420K of rattling motion with Γ3 symmetry.