We studied experimentally the mechanical properties of the red blood cell. By attaching beads biochemically on the cell membrane at diametrically opposite positions, the membrane movements can be detected very accurately, and a deformation of the cell can be imposed. A measurement of the mechanical properties at very small amplitudes is obtained by fluctuation analysis, and compared to the stiffness at larger deformations, obtained by stretching the cellsvia optical traps whilst monitoring the force. The cells are also probed at various conditions of pre-strain. These measurements show clearly a stiffening with strain and with pre-strain, which is strongest at low frequencies of deformation. The cell is measured to be slightly softer from fluctuation analysis, but consistent simply with the fact that the oscillation amplitude in fluctuations is very small. There is no evidence in these experiments of non-thermal sources of membrane motion, although non-thermal noise may be present within experimental error.