Optical registration technique is developed and frequency spectra are measured for dynamic shape fluctuations (flicker) in erythrocytes. Flicker spectra are studied in the range 0.03 - 500 Hz, using dynamic microphotometering of single cells in two optical modes: phase contrast regime, and reflection-mode laser probing. The registered spectra are similar to those typical of 1/f noise, with an essential difference: their slope in log-log scale varies with frequency, from -(0.8 divided by 1.2) below 10 Hz to -(1.6 divided by 2.4) above 50 Hz. The spectra measured with backward laser light scattering go systematically higher then those measured in the phase contrast regime. The theory of erythrocyte flicker is developed, based on the eigenmodes analysis of the bending oscillations of the cell envelope, and on the optical problem solution for the contribution from these oscillations to the registered signal. The theory describes quantitatively the spectral curves, and relates their parameters to the main mechanical and shape parameters of erythrocytes: bending modulus of cell membrane, viscosity coefficient of hemoglobin solution, and thickness-diameter ratio of a cell. The difference in the spectra obtained by coherent and noncoherent probing of erythrocytes is explained by specificity of optical mechanisms of the registered signal formation. No firm evidence is obtained for the contribution from the active processes in erythrocytes to the flicker.