Strains produced in the core of a multi-parameter Bragg grating sensor by transverse loading, axial loading or a uniform temperatrure change are computed by finite element analyses. The sensor is formed by writing gratings at two wavelengths in polarization maintaining fiber in which birefringence in the core is induced by an elliptical stress applying region. The finite element model accounts for the differences in geometry and mechanical properties of the different regions of the fiber. The computed strains are needed to determine the elements of a matrix that relates wavelength shifts of Bragg peaks to axial strain, two components of transverse strain and temperature change.