The two fiber gratings with two different wavelengths in a single mode fiber are bonded to the two neighboring side faces near the fixed end along the axial direction of a cantilever beam. Using the characteristics of fiber grating encoding, we have realized the measurement of the two dimensions for the stress or the displacement. The theoretical analyses and the experimental results indicate that the magnitudes and the directions of the stress, displacement and other mechanical quantities can be sensed and measured in real time through monitoring the value and direction of the wavelength shift of the two fiber gratings that are bonded to the near fixed end of the cantilever beam. In the vertical directions of the cantilever beam axis, the experimental sensitivities of the stress are 5.32 nm/N and 3.21 nm/N, the experimental sensitivities of the displacement are 0.30 nm/mm and 0.48 nm/mm, respectively.