The problem of reflection of plane waves due to an incident longitudinal wave at a plane free fibre-reinforced thermoelastic half-space has been investigated. There exist three types of plane waves which are longitudinal, transverse and thermal waves in the thermoelastic medium. The analytical expressions of their velocities are obtained and it is observed that they depend on the angle of propagation. Using appropriate boundary conditions, the amplitude and energy ratios for the reflected waves are derived and computed numerically.