The filtering and tuning properties of birefringent laser crystal are theoretically investigated. Using a matrix method and the given reflectance, transmittance coefficients in Refs.[12~14] by author, Fresnel coefficients on two boundary surfaces of filter plate are found. Using phase shift formulas and the ray tracing formulas, the accurate phase shift of filter can be calculated from incident angle and azimuth of optical axis. The Fresnel coefficients and accurate phase shift formulas of birefregent filter are used on the Jones-vector formalism and the eigenfunction of transmittance is obtained. The eigevalue is the transmittance of the waveplate. And the main filtering properties, in particular the transmission bandwidth, are deduced. The influences of the system parameters (incident angle, azimuth of optical axis and thickness of filter) on the filtering properties are discussed. Tuning properties are discussed using the accurate phase shift formulas. Finally optimum value of the parameters are derived. The optimum parameters are that thickness is about 1500～2000 μm, azimuth  is greater than 45° for quartz filter, number of round trips r is as big as possible lager, and incident angle is small as gain of laser is larger.