There is some axial extension in the applying scale of linearly chirped fiber Bragg grating(LCFBG) with transverse strain, which should be considered when the length of the applying scale is the same order of magnitude as the diameter of fiber. Based on the analysis of spatial elasticity, phase shift in the modulated refractive index distribution of LCFBG resulting from the axial extension is obtained. And the transmission spectrum peak created in grating spectrum is related to the value and position of phase shift. Furthermore, transverse strain can lead to birefringence. Considering all the factors aforementioned, the theoretical sensing model of transverse strain in small applying scale that can be treated as a point is introduced, in which the Stokes parameter characteristics of LCFBG are very important and useful. Simulation and analysis results show that the transmission coefficient grows exponentially with transverse strain but the peak value of transmission Stokes parameter spectrum is linearly dependent on the value of transverse strain applying in LCFBG. There is a one-to-one correspondence between the peak wavelength of transmission Stokes-s1 parameter spectrum and the applying position of transverse strain. And the peak wavelength of transmission Stokes-s1 parameter spectrum grows linearly with the value of transverse strain. So the position and value of transverse strain in small applying scale can be converted through the analysis method of measuring the transmission Stokes-s1 parameter spectrum of LCFBG.