Measurements are reported for epsilon(1) and epsilon(2), the real and imaginary parts of the dielectric constant, of Rb and Cs at room temperature in the frequency range 0.5-4.0 eV. The experiments were performed by multiple reflection at metal-silica interfaces employing the technique used earlier on Na and K. The optical absorption of Rb shows structure which can be attributed to conventional interband transitions within the nearly free-electron model. The optical absorption of Cs also shows structure, but the threshold occurs at a lower frequency than that predicted by the nearly free-electron model. Both metals show a leveling off and a perceptible rise in the absorption at the high-frequency end of the range. The possibility of absorption due to many-body effects or transitions to d bands above the Fermi level is discussed. The results for E, are used to deduce values for the infrared optical masses which are found to be 1.16 m for Rb and 1.19 m for Cs.