A new type of chirped fiber grating with cladding made of uniaxial crystal material whose optical axis is parallel to the axis of grating, i.e., z-axis, is proposed. Electrooptic effect and elasto-optic effect in this kind of fiber gratings are theoretically analyzed based on coupled-mode theory and transfer martrix. It was found that Bragg wavelength λB and the reflective spectra of the chirped grating can be changed by the electric field and the strain applied to the fiber grating cladding along z-axis. The curves of Bragg wavelength λB as a function of an external electric field or the strain are obtained respectively for three kinds of uniaxial crystals as the grating cladding. The calculated results indicate that when the axial electric field applied to the grating cladding varies from 1×107 V/m to 8×107 V/m, λB has the decrease of 0.12 nm, and when the applied strain varies from 0 to 0.04, λB has the decrease of 0.45 nm.