A method for manufacturing a fluoride crystal optical element comprising at least: providing a fluoride crystal having piezo-optical constants in a specified three-dimensional orthogonal coordinate system; converting the piezo-optical constants in the specified three-dimensional orthogonal coordinate system into piezo-optical constants in an arbitrary three-dimensional orthogonal coordinate system; calculating Δn1 and Δn2 which respectively are the amount of change in the refractive index of the fluoride crystal in a first direction along the direction of one coordinate axis of the arbitrary three-dimensional orthogonal coordinate system and the amount of change in the refractive index of the fluoride crystal in a second direction which is perpendicular to the first direction by using a uniaxial stress that is applied to the fluoride crystal along the first direction and said piezo-optical constants in the arbitrary three-dimensional coordinate system; determining the difference between the amount of change in the refractive index Δn1 and the amount of change in the refractive index Δn2 to determine the amount of birefringence with respect to a third direction perpendicular to the first direction and the second direction; determining the direction of observation showing a minimum birefringence for the fluoride crystal from the amounts of birefringence respectively determined in the arbitrary three-dimensional orthogonal coordinate system; and forming the fluoride crystal optical element by processing the fluoride crystal so that the direction of observation showing a minimum birefringence is caused to substantially coincide with the direction of the optical axis of the fluoride crystal optical element. providing a fluoride crystal having piezo-optical constants in a specified three-dimensional orthogonal coordinate system; converting the piezo-optical constants in the specified three-dimensional orthogonal coordinate system into piezo-optical constants in an arbitrary three-dimensional orthogonal coordinate system; calculating Δn1 and Δn2 which respectively are the amount of change in the refractive index of the fluoride crystal in a first direction along the direction of one coordinate axis of the arbitrary three-dimensional orthogonal coordinate system and the amount of change in the refractive index of the fluoride crystal in a second direction which is perpendicular to the first direction by using a uniaxial stress that is applied to the fluoride crystal along the first direction and said piezo-optical constants in the arbitrary three-dimensional coordinate system; determining the difference between the amount of change in the refractive index Δn1 and the amount of change in the refractive index Δn2 to determine the amount of birefringence with respect to a third direction perpendicular to the first direction and the second direction; determining the direction of observation showing a minimum birefringence for the fluoride crystal from the amounts of birefringence respectively determined in the arbitrary three-dimensional orthogonal coordinate system; and forming the fluoride crystal optical element by processing the fluoride crystal so that the direction of observation showing a minimum birefringence is caused to substantially coincide with the direction of the optical axis of the fluoride crystal optical element.