As a fundamental approach to studying elastic wave behaviors in fiber-reinforced composites, this paper introduces the analytical method to predict the modes, directions, and amplitudes of all reflected waves that are generated by free-surface reflection in fiber-reinforced composites. The paper also explores a new phenomenon where a reflected wave that is predicted to exist in accordance with the slowness surface may disappear. This may occur when the angle of incidence of a quasi-shear wave exceeds a newly defined critical angle, named the third critical angle. It is hoped that the analytical approach introduced in this paper will provide an easy-to-follow guideline for researchers in the relevant area such as ultrasonic nondestructive testing.