The acoustic phonons of the epsilon polymorph of 2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazatetracyclo [5.5.0.0(5,9).0(3,11)] dodecane (epsilon-CL-20) have been studied using Brillouin scattering spectroscopy. Analysis of the acoustic phonon velocities allowed determination of the complete stiffness tensor for this energetic material. The results are compared to a theoretical determination of the epsilon-CL-20 elastic constants, bulk moduli, and shear moduli. The observed ordering of elastic constants, C(22)>C(33)>C(11), is noted to be different from other nitramine energetic materials. Finally, the elasticity of epsilon-CL-20 is compared to recently published reports on cyclotrimethylene trinitramine's (RDX) elasticity and the beta polymorph of cyclotetramethylene tetranitramine's (beta-HMX) elasticity.