The polarization behaviour of radio waves which have been transmitted and reflected at or near normal incidence in an ice sheet can be explained if the ice is assumed to be a uniaxial birefringent material. Equations are derived for describing the change in polarization for the experimental conditions usually encountered when sounding ice sheets. One of the initial unknowns which can be found is the direction of the effective optic axis which determines the basic reference frame. Other parameters which can be found and related to the physical nature of the ice and reflecting surface are the total phase shift between the ordinary and extraordinary rays and their relative amplitude. The operation of several different types of polarimeter is discussed in order to compare the amount and the quality of information which can be obtained for various degrees of complexity in equipment and technique.