In order to study the change of Marple-Hess prism's transmittance with the incident angle observed in the experiment, all parameters related the prism are put in the mathematical model of three-point coaxial system. The Fresnel formula and multiple-beam interference theory are used to study the interference's effect on the transmittance in detail which is caused by first order beam and other order beams produced by reflection of air gap. A precise transmittance formula is deduced which can explain the phenomena that transmittance undulates periodically along with the plane incident angle's continuous change in the experiment. The theoretical curves of transmittance undulating with azimuth angle is also drawn, which indicate that the change of transmittance with azimuth angle is periodical, and the frequency and amplitude of the transmittance's fluctuation increase with the increase of plane incident angle's absolute value.